Since you two are sexually active and it sounds like he calls you his girlfriend in private but not in public, I would say he is trying to look good in front of you while keeping his options open.
He could be playing house with you, testing out the idea of a relationship in private while enjoying single status in reality. Yes, he could be only seeing you but until a guy says he is in a relationship with you and calls you girlfriend to all, well he can throw that back in your face if he starts chatting up another girl and you try and call him out on that.
Personally, sex before relationship is putting the cart before the horse, and this is an example of why. He is now sitting on the fence, able to enjoy both worlds while you wonder what is going to happen. As enjoyable as sex is, it doesn't make a relationship and it doesn't get a guy to consider one either. We all have dry spells without sex and it doesn't kill anyone to go without, so it is much better to put that to the side while we develop the connection it takes to want to be in a relationship. Now you are stuck actually having to say something about it if you really want this stalemate to end. Otherwise, endure it for as long as you can. Good luck!