Earlier in the week, my boyfriend broke up with me. We got into a small fight, and he called me over the phone to say that we were over, no longer in a relationship, etc. He didn't respond to my messages, and when I called him, he said he'd block my number and shut off his phone if I kept trying to call him. We weren't talking after that.
Later in the week, I was playing music for this small public event. This guy I knew came to see me, and there was a bit of sexual tension between us. He didn't stick around for long, but he asked me to walk with him to his car. I agreed. It was cold, and I forgot my jacket. He offered me his sweatshirt and put his arm around me as we walked. When we got to his car, we briefly kissed.
A few days later, my boyfriend got in contact with me, and upon discussing things, said he "never broke up with me." However, as stated above, he made it explicitly clear that it was his intention to do so. I didn't tell him about the kiss.
I'm not sure whether or not I feel guilty about what happened, and I'm not really sure where to go from here. I don't know if I want to be in a relationship anymore. Things just feel different between us. I told him that things between us just felt off, and I mentioned the idea of an extended break. My boyfriend started crying, begged me not to break up with him, and talked about killing himself, stating that every decision he ever made in life was a mistake. Even just sitting next to him, he was emanating absolute misery. I don't know what to do. I'm worried about him hurting himself.

At the same time, I don't want to essentially punish myself by staying with him out of pity.