Horse has gutteral pouch infection. What should I do?

When I brought my horse (8 year old appendix-quarter-horse gelding) to South Florida (88 degrees) from Maryland (50 degrees) in January, I noticed clear/white discharge coming from his left nostril. The vet gave him a general anti-biotic and it seemed to clear up but it came back.

Then he got two more oral antibiotics. No big change. Then the vet placed the anti-biotic directly in the gutteral pouch on 4 separate occasions in the span of a couple of months. It's starting to subside now. But, still some discharge.

The vet says if it doesn't clear up, an x-ray is the next step to determine if my horse has an abscessed tooth that can't be seen with a spectrum (which he's already had by the equine dentist who floated his teeth).

So, I'm wondering if the temperature here in Florida is to blame. What do you think?

And, what course of action should I take going forward?

What do you think of the vet's advice?