Hey Ziel, sorry i just now found your thread...I'm glad you did the responsible thing and got her to the Emergency Vet, as Budgies usually don't have much time left once they start exhibiting outward signs of illness. They are one of the best at hiding illness, and she has probably had that fungal infection for quite a while, and you would have had no way of knowing...
What medications did the Vet put her on? Did the Vet mention anything to you about adding a daily Probiotic to her food from now on? If not, it's definitely something that you want to consider doing, and should talk to your Avian Vet about next week.
I'll give you my experience with Probiotics and tell you that I HIGHLY RECOMMEND that you and everyone else start giving them to your birds on a regular, daily basis, as they will not ever cause any harm to your birds, but they can help them immensely.
As you mentioned, you NEVER want to give your bird any "vitamins drops" in her water, nor do you EVER want to put any medications in your bird's water, such as powder antibiotics, antifungals, antiparasitics, etc. There are few reasons for this, the main reasons are #1 Because you have absolutely no control at all over the dosage of whatever it is that your bird is getting if you put it in her water, so it's extremely unsafe, and #2 Because it will quickly and sometimes instantly, depending on what it is, taint your bird's water and cause health issues that you wouldn't have had otherwise...Mostly it's because you're not going to do your bird a bit of good by adding an Avian "Vitamin Drop" into their water at all. If your bird is eating a regular, healthy diet, and for a Budgie that means a Fortified, healthy, low-fat seed-mix that contains no sunflower-seeds, along with fresh Veggies and/or Dark, Leafy Greens (Budgies tend to like the Dark, Leafy Greens more than they do actual "vegetables"), like Kale, Mustard Greens, Turnip Greens, Dandelion Greens, Swiss Chard, Collard Greens, Romaine Lettuces (never feed any Iceberg or "watery" Lettuces), etc. I actually hang large pieces/leaves up from the cage bars of my Budgies aviary with clips, and they all just go to town on them...As long as she is getting a good diet, she doesn't need any added Vitamin Supplementation....HOWEVER, if you really do want to provide your Budgie or any other birds with a daily Multi-Vitamin, then you can actually do it in a safe, responsible way....
*****Again, you never want to add any Vitamins, medications, or anything else to her water, because you cannot control the dose that she's getting, and because all of those "Vitamin Drops" contain the Fat-Soluble Vitamins (A, D, E, and K), it's extremely unsafe and unhealthy to just put an unknown dose of them into her water, as these Fat-Soluble Vitamins are not excreted from their bodies, but rather stored in their fat, and in such a small bird as a Budgie, this can result is Vitamin-Toxicity very, very quickly, which can cause all kinds of secondary conditions/diseases....And just an FYI, on the opposite spectrum, you're also giving her an unknown dose of Water-Soluble Vitamins (B, C), which are just all being excreted out in her urates, and doing no good at all. You also are giving an unknown dose of all of the Minerals in those Vitamin Drops, which in such a small bird can result in everything from Kidney/Bladder Stones to heavy-metal poisoning...So putting anything in her water in an unknown dose is really bad news...
*****HOWEVER, they do sell daily Avian Multi-Vitamins that are not liquid, but rather powder, and that come with a pre-measured scoop inside of the bottle, so you are giving your bird a metered-dose of daily Vitamins, and these Avian Vitamins ONLY contain the essential Vitamins and Minerals that pet birds tend to lack in their daily diets when living in captivity, and not just any and all vitamins and minerals in unknown quantities like the cheap, liquid Vitamin Drops do. Those Vitamin Drops are sold at Walmart, Grocery Stores, etc., and they contain just a mish-mash of any and all available vitamins and minerals found in human multi-vitamins...In contrast, the more expensive, powder Multi-Vitamins only contain the vitamins that captive birds tend to lack in their diets, and contain no minerals that can accumulate and cause problems...Qwiko makes the best one that I've found, it's a daily pre-measured powder that is specially formulated for captive birds on a commercial seed/pellet diet, and you simply put one pre-measured dose of powder on your bird's seeds/pellets once a day when you give them new pellets or seeds. They ingest the powder when they shell the seeds or eat the pellets. I think a bottle of Qwiko Avian Vitamin Powder costs around $12 at Petco, and it lasts forever, as the pre-measured dose is very small. It's extremely safe, you're not contaminating your bird's water, and you're only giving your bird the vitamins and minerals that are essential and typically lacking in their daily diets, especially if they are on an all-seed diet and not eating any Fortified Pellet...HOWEVER, if you are also feeding your bird a Fortified Pellet, then you don't need ANY vitamin/mineral supplement...SOMETHING ELSE TO TAKE NOTE OF: I don't know what seed-mix you feed your bird, but there are several brands of Budgie seed-mixes that are actually ALREADY FORTIFIED WITH AN ADDED POWDERED MULTI-VITAMIN/MINERAL, so if you're feeding a daily seed-mix that already has an added Multi-Vitamin, then again, there's no need to give her any extra Vitamin supplement, as you'll only end-up causing issues with Vitamin Toxicity. I know that most of the Kaytee brand Budgie seed-mixes, specifically the "Forti-Diet" seed-mixes already have both a powdered Multi-Vitamin AND a powdered Probiotic supplement added to them...you just have to check the bag of whatever seed-mix you're feeding...
****Now, as far as a daily Probiotic, this is something that I believe strongly in and that I have been providing to each of my pet parrots as well as my breeder's every single day for years and years, and I can tell you that not one of my birds have EVER had a Fungal/Yeast Infection, nor have any of them ever had any type of Gastrointestinal Issues...Their Gastrointestinal Tracts, just like ours, are full of normal, healthy Bacteria that is supposed to be there, and who's job it is to keep their GI Tracts (from the Crop to their Cloaca) healthy, and also free of any type of Fungi, including yeast. This healthy, normal Bacteria attacks any Fungi that may enter their GI Tracts, whether from contaminated food, from yeast that has grown on their food inside of their cage due to moisture, or from a Fungal Infection that they might contract from another bird, other animal, or from a person who is infected with it or who has it on their hands, etc. (Fungi/Yeast can be spread from people, animals, etc., just like certain Bacteria can)...Also, ANY TIME YOUR BIRD IS PUT ON ANY TYPE OF ANTIBIOTIC FOR THE TREATMENT OF A BACTERIAL INFECTION, THAT ANTIBIOTIC WILL NOT ONLY KILL-OFF THE "BAD" BACTERIA THAT IS MAKING THEM SICK, BUT IT WILL ALSO KILL-OFF ALL OF THE NORMAL, HEALTHY BACTERIA THAT IS SUPPOSED TO BE THROUGHOUT THEIR GI TRACTS! This is the main reason that birds, dogs, cats, and yes, people often develop a Yeast Infection whenever they take an Antibiotic (i don't know if you know this, but women very often develop Yeast Infections whenever they take a course of Antibiotics, especially a broad-spectrum Antibiotic)...
****Probiotic supplements contain a mix of the normal, healthy strains of Bacteria that normally live inside the GI Tracts of most-all mammals, birds, reptiles/amphibians, rodents, marsupials, etc., and they contain them in extremely large quantities. That way, if someone is actively taking an Antibiotic, it can kill-off all of the residing healthy Bacteria in the GI Tract, and then even some of the extra added by the Probiotic, and there will still be enough from the Probiotic to keep the GI Tract free of Yeast and other harmful Fungi. In addition, Probiotics will also help to calm/neutralize any GI disturbances that can cause a lack of appetite, acid reflux, vomiting, etc. With birds, they very often end-up with Fungal Infections (yeast and others) inside of their Crops, because the Crop is a warm, moist "holding-tank" where food that they eat is held and made wet, and is prime real-estate for Fungi. So by adding a daily Avian Probiotic powder to your bird's food, just this can prevent your bird from EVER contracting a yeast or fungal infection, and will also keep their GI Tract healthy, calm, and your bird's Crop protected from the risk of Fungal growth (which can and does easily spread from the Crop throughout their GI Tract, as well as into their throat, sinuses, ears, eyes, etc. right from the crop)...I have been using giving all of my birds an Avian-specialty Probiotic powder on their food for about 10 years now, every single day like clock-work, and I've not had to take any of my birds to their CAV for any reason other than their regular, yearly wellness-exams. Not one of them has had any type of GI/Fecal/Crop/Upper Respiratory/Sinus infection, neither fungal or bacterial. So if it ain't broke, don't fix it. And a daily Probiotic can not harm your bird in any way, it can only help...so why not...