I also keep bettas in large bowls, maybe I can help a little too. Keeping them clean is key, as already advised. If you can do a daily water change, at least 50% (I do 100% every other day as a regular schedule if keeping a betta in a bowl) this should help immensely. If you feel the need to use a medication, a drop or 2 of methylene blue is a good one to use. I use this as a standard preventive treatment with all of my bettas when they first come home, as do many pet stores and even breeders. When they are shipped, most are shipped in this mixture as a preventive.
Please note that bettas are extremely sensitive to medications, and many are highly toxic to a betta. If you are worried about fungal issues, to make the medication effects stronger and more "well rounded", the methylene blue can be mixed with fungus eliminator. The safe way to do this is to premix medicated water in another, larger container so as to dose it properly. I use a 3 gallon bucket when doing this. Once mixed, replace 100% of the bowl water with the medicated water, changing it every day. Once mixed, the medicated water can be kept for up to 24 hrs and used safely, so you should be able to get 2 water changes from each bucket mixed.
I would use the medicated water, changing daily, for 5 - 7 days, even if you see improvement within the first few. This is the most effective well rounded and safe medication that exists for a betta so far that I've found, and my experience at the store has given me the chance to work with almost every medication out there, and this with most of the available species of fish on the market. If you need more help, let me know. In case you are in doubt, I had a female betta with a stomach injury. Her bowl cracked, and she injured herself on the gravel when the water drained out during the night. She had an actual hole scraped into her side. This fish was almost 5 yrs old at the time, so I thought for sure she was a goner. Not only did she heal up great, but she had minimal scarring from it and lived almost another year! She was my oldest betta yet. The only medication I used was the methylene blue, with the schedule I described for you here. I have been keeping and breeding bettas for more than 10 yrs now, and have nursed hundreds back to health in that time. I know exactly the symptoms you are describing, though I am at a loss to name the problem off the top of my head at the moment. Keep your fish warm and clean, that is most important, especially in a bowl environment with no filtration. Also, be careful not to overfeed. About 5 pellets every other day is plenty, but no more than 3 - 5 pellets once/day. Their stomach is about the size of their eyeball, and they need time to properly digest the food before receiving more. Overfed bettas will often experience stomach problems and polluted water issues. I hope he gets well soon!