I would be surprised if you couldn’t get a pharmaceutical alternative to allopurinol in a neighboring country if not in Belize.
Teijin (The Japanese company which developped febuxostat) claims it is available in Belize. But Belize being such a small country, they could of course have their facts wrong. Maybe you could contact them. I did have a quick look on the web and found pharamcies claiming to stock a Latin American brand of febuxostat in Guatemala. Did you look for Latin American brands as well as Uloric (the gringo brand)?
As to probenecid, it’s only one of a type of drug called uricosuric. You could look for others (keeping in mind that in Central America drugs might be sold under a variety of brand names). I should however warn you that this class of drug is not appropriate in every case and is usually not as effective as allopurinol and febuxostat.
I don’t know about herbal medicines but there are dietary choices which are correlated with lower uric acid. With your uric acid at 7.6, it would likely be difficult and very slow to get good results that way but it’s not totally hopeless. Certainly it would be better than doing nothing.
Do tell if you want more information about that but I have to stress that febuxostat works much better.