My boyfriend's best friend is my ex! Please help ?

Okay so my boyfriend's best friend is my ex! We went out two or three times and every time I broke it off because I liked his best friend (my current boyfriend). Its really awkward to be in the halls with my boyfriend and his best friend at the same time. I mean i can't even sit at the same table at my boyfriend because he's there and I feel really uncomfortable around his friends. My ex knows that I still like him (I mean I do but I love my boyfriend so i'm not breaking up with him anytime soon!) and right before we broke up he gave me his jacket. I've asked him if he wanted his jacket back and he said no with a smile. Well I think I should give his jacket back to him but i would feel really awkward. Anyways I just don't know what to do, the guy is always around me it seems but when we were dating he was like never around so I don't know if its just my imagination or what! But the guy is always around me and when ever I am going past him to go into my class or to go to my friend's locker with her he always just perks up and starts flirting with another girl. And when I'm around my boyfriend or if I'm talking to him the guy comes up and jumps on his back and starts choking him (as in the guy likes to fight him but hes never mad and my boyfriend always laughs afterward of kicking his butt.) And hes mad strong so he almost made my boyfriend faint by choking him. Anyways what do I do? Or more importantly am I over thinking this whole thing?!