Should I dump him?

So I started dating this guy a month ago and I'm thinking about breaking up with him. New years <a href="https://play.google.com/store/apps/details?id=com.glow.android.eve">eve</a> he was hanging out with his neighbor and I asked him if he planned on hanging out with her til midnight (I was just asking as a conversation piece) and he asked me why I was being that way which confused me and I asked him what he meant and he started going off saying he doesn't like I'm acting jealous because she's his only friend and then said I think we should break up because he doesn't have to deal with that shit and I just sat there staring at the messages for a second shocked before I even responding because I was not even saying anything about him hanging out with her. It was literally just a question. I was like are you serious right now? It was just a question I wasn't being jealous at all. And he said you pissed me off so much I deleted all of our photos and then a bit later he asked me if we were still together and I was just like wtf 🤦‍♀️.. I just said I would like to be and then he apologized and started acting like nothing happened. It was the weirdest thing. Now every time he is going to hang out with her he tells me like he's waiting for me to say something about it and honestly it's just getting annoying and after his little crazy fit I just don't feel the same about him. He is schizophrenic so maybe that's what his problem is? Idk as I've never dealt with someone like that but we live 2 hours from each other and the distance is getting to me anyways because my car is currently broken down til I get a new battery for it and he surprisingly never has gas money to come this way.