Just to give you my view since I'm in a dorm room and can't have a tank, my first input is you're feeding him too much. I have my bettas in a smaller space like you because, also like you, that's what I can afford and am allowed to have in a dorm. You'll have to clean the tanks more often, but you'll get the hang of it. Only feed them maybe twice a day and not very much. I usually feed mine in the morning when I leave for class and around dinner time.
Now before people go yelling at me for saying it's ok to have a small tank, I'm in the same boat as 3ltonWorri3s. I cannot afford a bigger tank right now nor do I have the space, but with proper care your betta will be ok until you get him a better home. My 2 bettas are very active and healthy.