Okay, you need to take a minute and think here...No more medications without a diagnosis, as she's had too many already and they can make her just as sick or worse...
***If this Vet thinks she "might" have a tumor, then the next step is doing a simple plain-film x-ray of her, they get the entire body at once, it doesn't cost much, and that will IMMEDIATELY ANSWER THE TUMOR QUESTION, NO QUESTION AT ALL. When you x-ray a bird you get the entire body, so not only will they get her entire head, BUT ALSO HER LUNGS AND RESPIRATORY TRACT, which will also show if her lungs have any masses, fluid, congestion, etc. This should be automatic at this point, and honestly should have been done weeks ago with the URI symptoms she's had...
I really got to tell you that this Vet is probably making things worse for her. This Vet has already spent weeks NOT doing diagnostics and just shooting her full of meds. I don't like it...And I'm willing to bet that this injection is a Steroid?
Here's the deal: Without knowing whether she actually has "a mass", which could mean a cyst, an abscess, a tumor, or many other things, if this Vet just goes ahead and gives her a Steroid injection once a week they could actually make certain growths worse. Plus, let's say she has something that actually needs to be treated soon or it's going to either grow so large that it impedes her breathing, a nerve, etc., or that it could actually rupture without simple treatment. So this Vet goes ahead and starts Steroid or anti-inflammatory injections, which do nothing, and your bird dies in the meantime of something that could be treated, but because an x-ray was never done you'll never know about it...
My biggest issue here is that a simple plain-film x-ray is usually one of the very first things that are done with a bird having URI/lung or sinus symptoms, and honestly I thought, or maybe just assumed that they had already done an x-ray at her very first appointment and found that her lungs were clear with no fluid or congestion/growths, and there were no growths or abnormalities anywhere else. So I didn't even mention it...Seriously, my Quaker Parrot had a horrible Upper Respiratory Infection almost 2 years ago, I made an appointment with my CAV the minute I felt something was wrong, and her symptoms on the day I took her in were "an occasional sneeze and/or cough maybe 5-10 times a day". That was it. She had no nasal discharge, no mucous in her mouth, she didn't "look" sick, she was eating, drinking, playing, flying, etc. all normally, she was just coughing and sneezing once in a while. No wheezing or breathing issues...And when we got to her very first appointment with my CAV, he weighed her, did a complete and thorough physical exam/visual exam, and then he said "Ok, well let's get some cultures from her nares, throat, and then a Fecal too just because we should while she's here, and let's get a normal radiograph to look at her lungs, her sinuses, her air sacs, and her ears". And 30 minutes later she was back, x-ray was clear, no lung infection/pneumonia or masses anywhere, and he said he saw bacteria and white cells under the scope from her nare culture/flush, and we got meds to nebulize...But the x-ray (radiograph) was the first thing he did...
So bottom-line here, and this should make sense to you, is IF this Vet actually told you that your bird might have a "mass" or a "tumor" somewhere in her sinuses, the very next words out of her mouth should have been "I want to get an x-ray to confirm or rule this out.", not "Let's put her on yet another medication on a "wait and see if it helps without knowing what is wrong" basis"...I can't even believe that they wouldn't have already done an x-ray with as long as she's been sick with respiratory symptoms, GI symptoms, etc., I just assumed that an x-ray had already been done and was clear...
****And as far as the "anesthesia" for doing an x-ray goes, it's extremely safe. They use an ultra-short-acting gas that literally lasts just long enough for them to shoot an x-ray and that's it. It's not anything like regular anesthesia like you're thinking, like they use for surgery. They literally take the bird in the back, put her head inside of a clear, plastic "cone" that is hooked-up to the gas, your bird slowly falls asleep in 30 seconds to a minute, they rush her over to the x-ray machine, put her on the plate and stretch her wings/legs out so they get her entire body, they shoot the x-ray, and then they usually will hold them in a towel until they wake up fully, and put them in a heated incubator for maybe 10 minutes or so if they're cold, if not she comes right back to you. That's it. I've had it done to all of my birds, including my little Budgies, as they all go to my CAV for a full Wellness-Exam once a year that includes an exam, a Fecal Culture, routine Blood-Work, and an x-ray. And honestly, if this Vet is that concerned about your bird even being put-under with the Iso gas in order to take an x-ray, then they should know that it is very possible to take an x-ray of a little bird like a Cockatiel while they are awake, especially a sick one that isn't as frisky as normal. All it requires is two people,
one to hold her down on the plate and the other to hold her wings out, and often they actually have the owner be one of the people because it helps to keep them calmer. And in this particular situation it's just that important that an x-ray be done...
Listen, I know you are worried to death and totally frustrated, and honestly I'm frustrated beyond belief with this Vet of yours, because I cannot believe that your poor little Cockatiel has been this sick with respiratory symptoms for so long, like what, 2 months long?, and the very first thing they did was give her Doxycycline shots for multiple weeks without doing any tests at all, not even a Fecal or a sinus culture, and then when multiple weeks of the Doxycycline guess didn't work, THEN you had to come here for information and then go in and actually tell the vet that you wanted the most basic diagnostic tests done instead of just pumping her full of more prescription medications on a hunch or a "try and see" basis; And now that the most basic diagnostic tests showed nothing, now this Vet told you that "she might have a mass",
and wants to shoot her full of more medications ON A GUESS, without doing a simple x-ray that would 100% rule-out or confirm "some kind of mass" anywhere in her body,
and would also show whether or not her lungs have any fluid, masses, etc. along with her air sacs, and also show whether her liver is enlarged, her kidneys are enlarged, whether her UR tract and/or her GI Tract is inflamed, etc. It's time for this Vet to stop guessing...
Is there another Certified Avian Vet or Avian Specialist Vet that you can get a second-opinion from? That would be exactly what I would do, like right now. You can have all of her records and all of the test results like the blood-work and the cultures sent right over to the new Vet's office digitally, so that will save the new Vet from doing any of these tests again (unless they see something that this first Vet missed in the results), and the new Vet will also have a record/list of all of the medications this vet has put her on, the doses, the length of the rounds, etc., so assuming that you can find a CAV that knows what they're doing, they'll be able to look at what medications/antibiotics she's taken and be able to tell just from that what conditions she doesn't have...That's exactly what I would do, and what most people would do at this point BEFORE shooting your bird full of more meds on a "try and see" basis...
****I would look at it this way: This Vet gave your bird multiple shots of Doxycycline without doing ANY tests or having any idea what was wrong with her, right? And what happened as a result of that first guess they made? Well, not only did the Doxycycline not help one bit because it was not necessary since she doesn't have a Bacterial infection at all, so she took a very strong, potent antibiotic for weeks and weeks for absolutely no reason, AND IT CAUSED HER TO DEVELOP A FUNGAL INFECTION THAT SHE WOULD NEVER HAVE GOTTEN!!! And now this same Vet is going "Maybe she has a mass, no way to know, but let's now put her on ANOTHER DRUG ON A GUESS by injection once a week, and let another month go by with your bird suffering, not knowing whether THIS DRUG will help or not, will make her worse or not, will cause new issues or not, and in the meantime we'll let another month go by with her suffering. Do you understand where I'm coming from? This Vet is once again doing the same thing, she's guessing and doing the "try this and see" thing again. This time with steroids. You can't do this to her again...I mean, you can, she's your bird, but it makes absolutely no sense to do the same thing again that you were so angry about before...You were pissed when you realized that this Vet had no idea what was wrong with your bird, had done no tests, and had pumped her full of drugs on a guess/try and see basis for weeks and weeks. So why would you do it to her again? And this time with a type of drug that can cause her kidneys great damage, among other problems, such as "Cushings Disease", which is often a result of long-term steroids or cortisone shots.
She's your bird, but this is ridiculous now. Either demand that this Vet take an x-ray BEFORE giving her any other medications for a "pretend mass" that may or may not exist, or better yet take her to a different Certified Avian Vet, have her records/test results transferred to the new CAV, and get a second opinion. And we can help you find the nearest CAV to you...