You may be overfeeding your betta. I feed my boys 2 hikari micropellets (they are little smaller than betta pellets) in the morning 2 at night, once every few days bloodworm or daphnia and once a week I don't feed my boys at all. Is your bettas tummy big and round? if so, you may want to try cooked peas (not the skin) to help him to "go to the bathroom" and do not give him any pellets for few days at all to see if his bloating goes down and his swimming improves. Fish can go for about a month without the food, so don't worry, he'll be fine if you stop feeding him for few days.
Since you don't have a heater and no idea what the temp of the water is, you may at least want to keep him in the room with stable temperature (prefferably above 72 if possible)
If you have any pics, that would be helpfull.