Well, I agree with your vet about there possibly being something in her nose - that was one of my first thoughts. However, I wouldn't say that or a brain tumor are the only other options. Certainly some sort of tumor is a concern, given her age, but it might be something in the nose or sinus
cavity. I would expect other symptoms than just the sneezing and nasal discharge if it were a brain tumor.
So far, it sounds like he has been treating her for a bacterial infection. You could also be dealing with a viral infection or allergies. Although 12-13 years old is pretty old to start having allergies. But they don't always read the book!
Clavamox is generally a good antibiotic, but I don't usually have a lot of success with it in upper respiratory infections
. URIs in cats are usually caused by one (or a combination) of the following: herpesvirus, calicivirus, chlamydia (now more properly called chlamydophila - and is a type of bacteria), mycoplasma (another type of bacteria), and bordetella (yet another bacteria). All of these bacteria are kinda "picky" about what antibiotics they are susceptible to. Clavamox will sometimes work, but not nearly as often as others, such as tetracycline, doxycycline, or azithromicine. I usually use Doxy first, and then if they don't get better on that, will consider azithromicine - but I rarely have to go beyond the Doxy.
Now, since she did respond to the azithromicine, I would say there was definitely a bacterial component. But, since it hasn't completely resolved, I would guess there is another component to the problem - something that made her susceptible to the bacterial infection.
It could be an underlying viral infection. A lot of cats get exposed to either herpes or calici, and either never get sick or "get better" but remain latent carriers. In those cases, if something happens to stress their immune system out (such as coming down with another systemic illness like hyperthyroidism), they can have a relapse. There really isn't anything easy that I know of to do for calicivirus, but fortunately, herpesvirus is much more common than calici.
For herpesvirus, there is something you can do which can help. The herpesvirus requires the amino acid, arginine, in order to replicate. If you supplement your cat with L-Lysine, it blocks the arginine receptor and prevents the virus from reproducing. Lysine won't "kill" the virus, like antibiotics are supposed to kill bacteria, but it will stop the virus from progressing and give the cat's immune system a chance to take care of it. You can get l-lysine from most drug stores. The dose for a cat is 250 - 500 mg twice a day. I usually recommend getting the capsules and just opening them over the cat's food
, or if you can only find tablets, crush them and sprinkle them over the food. If her problem isn't herpes, the lysine won't hurt. And if it is herpes, you should see at least some improvement in a week or so.
The other possibility I mentioned was allergies. Now, I really wouldn't expect a cat to suddenly come down with allergies after 12 years of never having a problem, but it's worth checking out before going through a lot of expensive testing. Since this has been going on for months, I would say you can probably try one thing at a time so you know what actually worked. Since herpes is more likely than allergies, I'd try the lysine first. If you don't see any improvement on that, then talk to your vet about putting her on an antihistamine for possible allergies. My preference is chlorpheniramine (brand name Chlortrimeton). That's actually what my own allergic cat is on - but he has skin problems rather than respiratory. The advantage to using an antihistamine instead of a steroid is that if it's an infection rather than allergies, you're not going to make it worse.
Which brings me to another thought. Since this all seemed to start when she started drinking from the faucet - it's possible that it is something up her nose, just not what we'd normally expect. She could have gotten some sort of mold up her nose, either from the water or sniffing at the faucet. In that case, an antifungal medication would be indicated. But I wouldn't advise that without knowing exactly what you were dealing with, since most of the antifungals can have some serious side effects.
So, that brings me to my next suggestion. If neither the lysine or antihistamine help, then the next step would be to have some diagnostics done. Rhinoscopy, where they run a fiber optic camera up into the nose and sinuses, would be the ideal. However, I don't know how likely you would be to find someone in your area with an endoscope small enough to go up a cat's nose. An alternative would be to have a sinus flush done, and then have that cultured. That would serve 2 purposes - the flush alone may help wash out whatever is irritating her nose and sinuses, and if not, the culture would tell you what "bugs" you have going on up there that are causing the problem. I'd just suggest making sure they run a fungal culture as well as a bacterial. Another thing to be done would be an xray of her head - especially the sinuses. That would help to show any masses (which could be a tumor, or an infection - especially fungal), and may show a foreign body - though I would expect that a foreign object small enough to get up a cat's nose may be to small to show on your average xray.
I hope this helps. Let me know if you have any further questions, and good luck with her.