Don't know where to start

My bf and I have completely different conflict styles. I like to talk about what's wrong, get everything out in the open and he just shuts down. Brick wall. And then my budging makes him even more upset then in the first place. If he had it his way we'd never talk anything out and that bugs me. I don't know what to do, but this really upsets me. We are currently in a fight and right now I pushed him to the point where he won't answer my calls or text back. Of course I sent him the clingy emotional texts, and of course they didn't help. I just don't know how much of this I can take. I always hope his reaction will be better but it never is and I'm left an emotional wreck while he's ignoring me playing video games. I can't even talk to him about this without him getting upset and shutting me out.