Is my Betta okay?? helo.....?

I just got my betta yesterday and now hes in a fish bowl(just one of those 4 doller plastic ones you buy at petsmart and ive been feeding him as much as his food bottle says to but he keeps swimming down to the bottom and just sitting on the bottom without moving his flippers just being still or some times he floats up to the top and he looks as if hes dead.. is he maybe sick or does you betta do that too?