The two things that you probably want to do are check your water parameters and treat the illness. (I'm saying this from doing a LOT of reading on betta illnesses, but I've never personally dealt with symptoms like your betta's).
What size of a tank is your betta in? And is it filtered and/or heated?
You'll want to check the ammonia/nitrite/nitrate. Ammonia and nitrite should be 0, and nitrate should be 10PPM at most. If any of these levels are too high, you might need to step up your water change schedule, consider a larger tank if he's in something smaller than 2.5 gallons, and/or consider a cycled tank if yours isn't currently cycled. (Fishless is, in my opinion, the best and most humane cycling method) Creating ideal water parameters is essential for healing and future disease prevention, as bad water conditions often contribute to or cause fish illnesses. Also, a temperature lower than 74-76 degrees is usually too chilly for a betta and will weaken their immune system, leaving them more vulnerable to diseases and less able to heal. So temperature of the betta's tank needs to be considered as well.
As for the illness itself, from what I've read, it's likely that it could be a bacteria - the symptoms sound to me like Columnaris, which you might want to look up and check the symptoms for. Cottony white patches are a symptom of this illness, and here's a link to a description of it from one site:
Note that this illness is sometimes nicknamed as a "fungus," but it is in fact a bacteria and should be treated as such. In the alternative, it could also be a fungus, but it was my understanding that a true fungus is less common in bettas than Columnaris - please correct me if I'm wrong.
And from the same site, here's an article on general disease treatment that I find helpful - it discusses a little more the steps you should take before launching into treatment of the illness itself.
Best of luck with your little guy, hope he's feeling better soon!