Well, for what my 2 cents is worth, I would say to keep him quarantined if you have a divided tank...you don't want to risk him infecting your other betta with which I'm 99.9% sure is a parasite.
From many betta owner testimonials, I've heard that Jungle Parasite Clear can help get rid of internal and external parasites. Jungle is probably one of the most recommended medications for parasites on multiple sites and forums. If you want to avoid medications, potassium permanganate is another way to treat the tank (a type of salt).
Note: From observation, your betta looks like it might have an anchor worm infestation...maybe the sore is a type of breeding ground which, in my prediction, will eventually burst