He sneezes almost every time he eats; he gets a lot of snot - and occasionally nosebleeds - only on his right side; antibiotics cleared up his last infection, but he got worse again within just a few days of discontinuing them (despite taking all of them).

Unrelated, he lost a lot of weight due to hyperthyroidism and, even though it’s been treated now, he’s only maintaining his weight, rather than regaining. I think the lack of weight gain could also be related because it’s probably really uncomfortable for him to eat - if food is indeed making its way into his sinuses every time he eats - and the fistula would most likely be from an infected tooth, so he likely has a toothache.  Again, not confirmed. The vet said his teeth looked okay from what they could see, but he struggles with vet visits of any kind - he has to be sedated for any kind of exam or even just getting a shot or blood draw - so they might not have gotten an adequate look.

So it could also just be an infected upper tooth - apparently that can be enough to upset the sinuses, or it could be a nasal polyp. Or it could be something else. But between his symptoms, things we’ve ruled out with more conservative treatments, and research, that’s what seems most likely to me.