Boyfriend talking to other girl

My boyfriend is snap chatting this other girl that he knows I do not like before he started talking to her. She gets mad when I’m in his snaps or if I snap her from his phone when he asks me to reply to his streaks. But lately I’ve been a little jealous and worried that he has something going on with her. So the other day I read through their conversations and he had sent her that “‘I like talking to you 😃” and when she sent him a picture of a fish she was holding he said cute. He then later sent a heart to her. I got very upset and my heart dropped I know this is not much to be worried about but still it’s just not something he would do. So later that night I asked him about it and I started crying. He looked at me and apologized and I asked why he said those things and he said he felt bad because she always snaps him saying she’s ugly and wants to kill herself. We then talked about it and he told me and got really serious when he said “ i love you and i mean it when I say I am going to marry you and I mean every thing I say to you” and I knew then that I couldn’t be doing anything behind my back. He then told me he would tell her that they couldn’t talk anymore and he did the next day. Should I be worried about this girl and him possibly trying to talk behind my back again or should I take his word on not wanting to hurt me and that he was just trying to be nice to her? I trust him but it’s hard not to forget about the things he said to her. What should I do?