i would check out the betta section of the forum, which you can also get to by going to Betta Fish and Betta Fish Care
its the same login, same members and everything. there are some really knowledgeable people there, and tbh i never even look at this part of the forum. if you post in the disease section they'll be able to help you
my advice, i would say get a heater, keep it between 78-82 degrees F, because they do WAY better in warmer water, and i believe they live in water in the wild that stays around that temp. also the only additives i'd use if i were you are prime, and since he's sick, some aquarium salt at 1 tsp/gallon.
i dont know much else about disease, but those are measure i'd take with a sick betta coming home. hope this helped, and that someone in the betta section can help!!