This is really aggravating.?

Alright, my boyfriend has a facebook. He met this girl before he met me and they've been friends. Thing is, he never actually met her in person. He randomly added her bc he knew people who knew her and he thought she was pretty. On facebook, she likes every status and every photo that he has. Shes pretty so i get jealous a little bit. She comments his pictures saying "cutie^-^" and i ask him to tell her to back off if shes just a "friend" and he did. She still does the same thing. I askk him again to tell her to back off. He says.. she hasnt done anything. I'm like.. why are you acting so oblivious to it? then he had the balls to ask me if they can hang out this summer. I'm like.. Honestly, i would say no but i'm not going to tell you who you can and cant hang out with. So he just said he couldnt hang out with her bc he knew id be uncomfortable. I mean, i have every right to not feel comfortable about it. Right? :/ He never met her. He thought she was pretty so they became friends. they text. she likes all of his photos. he told her she should take a picture for him bc he wants to see her smile. He has his friends adding this girl. Its like shes someone he wants to show off.. it really aggravates me because i'm insecure about it. I hate telling him because we argue about her all the time. So someone please help me! this is just such a stress for me. What do i do? he's a signed musician by the way so girls are always all over him. but this is the only girl he actually gives feed back to. ya know? :|