Hospital? No. There is really nothing in your posting that would indicate the need to go to a hospital. If you want to do something, throw away those Q-tips and he won't damage his ear next time.
Obviously, I have no way to look inside your boyfriend's ear to find the source of the blood. A tiny amount is probably from the ear canal (like you suspected); a larger amount of blood could come from a ruptured eardrum caused by the Qtip. Assuming he is not in pain or having any more bleeding, I think it would be fine to just let it be for now.