The first thing you need to do is put him in his own cage, and relocate him in his own cage into a totally separate room from your other two birds. Any time you bring home a new bird, regardless of where it comes from or how old it is, you absolutely must do a 30-Day Quarantine where the new bird is kept in it's own cage by itself, and the cage must be kept in a room by itself, away from all other birds already living in the house, and behind a closed door if possible. However, in this particular case, this Budgie came from an extremely neglectful, dirty, unhealthy environment, and he's exhibiting/displaying active signs of severe infection/disease, that is very possibly contagious to your other birds. So if you haven't already done so, you MUST put him in his own cage in an entirely different room from your other birds, behind a closed door if possible, and then you're also going to have to keep a very close eye on your other birds now for the next few months to make sure that they too don't start developing any infections, illnesses, or have any parasites such as Feather-Mites that it's very possible that this guy has due to his prior filthy home.
Now as far as the bumps on his foot and wing, can you please take some photos (close-ups of the bumps) and post them for us to see? And can you please explain what you meant by "The bumps at first showed signs of cancer"...Did the Vet you took him to tell you that the bumps showed signs of cancer? And if so, what was this Vet basing this on? Did the Vet take a culture/scraping of the bumps and look at them under a microscope? Did the Vet at least look at the fluid they drained from the bumps under a microscope? Send it out for a Culture? Also, as far as the "fluid" that the Vet has drained from this bump/bumps, was the fluid clear? Bloody? Or was it white/tan/brown and thick?
Typically cancerous growths don't just pop-up over night like this, nor do they fill with "fluid", nor do they fill back-up with fluid after they are drained. This doesn't at all sound like cancerous growths, but rather a severe bacterial infection of some kind that is causing Abscesses to form under the bird's skin. Abscesses develop rapidly, they fill-up with fluid that is usually a mix of mostly white blood-cells/bacteria (PUS) and maybe a little blood, maybe not. (This is why I asked if the Vet looked at the fluid they drained from the bumps under a microscope, as they should easily be able to see whether or not the fluid contains white blood-cells, bacteria, blood, etc., as well as what type of bacteria it is. This would instantly (or should have) tell the Vet that the bump/bumps are Abscesses due to an infection, and that the fluid is Pus, and should have indicated to the Vet that they needed to send-out a Culture of the fluid to the lab they use to determine exactly what strain of bacteria is causing the infection, and then exactly what Antibiotic will treat that specific bacterial. It may also be a Fungi that is causing the infection, which is identified the same way, by taking a culture of the fluid, looking at it under a microscope in the office initially, so that the vet at least knows whether it's a bacterial or fungal infection so that they can start the bird on a broad-spectrum antibiotic or anti-fungal medication, and then they send the culture out to a lab so they can specifically identify the strain of bacteria or fungi and the medication that should be used, and then the Vet can change the Antibiotic or Anti-Fungal the bird is on to the correct one that will treat the infection, if they didn't choose the correct one at the office appointment...A culture should only take 2-3 days to get results back from...Did the Vet do this?
Did the vet do a blood-draw from the bird's neck to run routine blood work, such as a Complete Blood Count and liver/kidney function tests? This is simple to do, and will tell the vet if the bird has any type of infection, how bad the infection is, and whether or not it's effecting his organ functions...
It sounds to me like unfortunately the vet you took the bird to has no idea what they are doing...I'm going to assume this was either a General Vet or an Exotic's Vet, and not a Certified Avian Vet or an Avian Specialist, correct? Can you tell us exactly what medications they put the bird on? Each of them?
My best recommendation is that you find the closest Certified Avian Vet or Avian Specialist Vet to you (if you have to drive a few hours one-way then that's what you have to do, because this is probably extremely urgent at this point), we can help you find the closest to you if you let us know what town/city and state you live in, and you get him there immediately. It sounds to me like he has a very serious, systemic infection at this point, that probably started in his foot (he may have had a cut/wound on his foot, or it may have entered through a toenail), due to his filthy, unsanitary prior conditions, then his foot got infected, he got no treatment at all for the infection in his foot, and now the infection has taken over his foot and will continue to spread up his leg and eventually it will become systemic...Now the fact that he also has the same kind of "bump" on his wing all of a sudden too tells me that the infection may already be systemic, or he just has several local infections all over his body, which is not uncommon for a bird living in the conditions that you describe. There's not a lot that we can help you with, but if you post some photos of both the bumps on his foot and the one on his wing, and any other ones you see, we might have a better idea as to whether they are local abscesses due to infection or not...
Did the Vet tell you to treat the actual bumps with a topical disinfectant and an antibiotic cream?
****Also, please stop putting any type of vitamin-drops, supplements, or any medications in the bird's drinking water!!! This instantly contaminates his drinking water with bacteria, fungi, etc., and in addition those cheap vitamin drops are not beneficial but rather harmful, as you have no idea how much he is getting of each vitamin/mineral because it depends on how much he drinks and how much is in his water, etc. So all this is going to do is make him worse-off. He needs to have a lot of fresh, clean drinking water at all times, and let him get all of the nutrition/vitamins/minerals he needs from his diet.
***Please tell me that the Vet didn't give you medications, such as the antibiotic that you're giving him, that you are supposed to put in his drinking water, did they? If so, then this is horrible and will not do a bit of good, and will only make him worse....For future reference with any of your birds, don't ever agree to put anything at all in their drinking water, no vitamins, no supplements, and especially no medications. All medications that your birds get should be given orally in liquid form, either directly into their mouths/beak from a syringe without a needle, or by you putting the liquid medication in a very small bit of a treat or food for them to eat, but never in their drinking water....
