Is my boyfriend still in love with his ex?

My boyfriends ex girlfriend just moved to our school and he hates her. I think she is nice but again she hates me. So we went out to eat and my boyfriend got mad bwcause she was there with her boyfriend and just when I was about to sit down he snatched the seat from under me and comes running to me to help me up then drops me and helps me up again. We started eating and she.comes over and tells him hi but when I tell her hi she tells me that she saw my nasty fall and it was almost like my nasty face. So I get up and start yellong at her and so does my boyfriend and so her boyfriend comes and starts yelling at him so we end up getting kicked out of the resturant. Then when we get to school I was talking to my boyfriend and she comes and he just throws himself on me kissing me. Then I was walking to class and I guess she was beside me and he comes out of nowhere running and trips and he falls on me in the bushes and we get in trouble for affection. I dont know what to do I really font want to break up with him.