Boyfriend Issues

I’ve been having a lot of issues with my boyfriend this past week. I’m 13.5 weeks pregnant and we don’t know if it is his or another’s mans child. And we’re betting mostly on it being the other guys child but he has said he wants to do this and be apart of our lives. He use to be a really bad drinker and I told him that it has to stop now because I can’t deal with the stress and he did for 3 weeks but this past week he’s showed up tipsy 3 times and I’ve told him listen I don’t want to hangout with you when your like this so I leave. And when I do that he gets angry and starts saying how I don’t appreciate him and how this isn’t even his child and that I don’t see how hard he has been trying. But that’s not true. I don’t know do you think I’m over reacting? I just am worried that once my little one gets here he’s going to be pulling this bullshit and showing up drunk and angry and I don’t want to deal with it or put my child In harms way. That’s why I told him that he can’t be showing up like this while I’m pregnant so he can prove to me that he’s capable of doing it.