Jealous of my bf's female friend?

My boyfriend and I have a very strong and serious relationship, we've even mentioned the possibilty of marriage after graduation, and we take eachother's feelings into consideration and never joke about them. But before he met me he had a met another girl who he never had a relationship with, but apparently became close friends with and she considers him her "best friend". I constantly get jealous of her because she always wants to spend time with him and be around him as much as possible. My bf told me she is a huge flirt and he admitted that she always tries to touch him and tried to hold his hand and acts as if they're together, and this girl herself has a bf. My bf told me he knows I don't like her, so he promised to stop being around her and talking to her. He said he doesn't care about her and cares far more about our relationship than ever speaking to her again. I always trusted my bf 100%, but I NEVER trusted her, my bestfriend knows her and told me the niciest thing to call her would be a whore. My bf totally agreed to stop his friendship with her permanently, but every time I hear her name this anger builds up inside me when I think about how flirtatious and forceful she was with my bf, and it makes me go crazy but I feel as if he's all mine and I want no other girl thinking he's somewhat her's. I feel like one day if I ever see her I'm just gonna blow up, I mean, is it normal for me to act that way?