My boyfriend cheated on but I've been bad to him. I don't know what to do. Please help?

We started dating last year in September. He's 21 & I'm 19. This year has been amazing but very stressful. We used to fight a lot over stupidity but when we're good, we're really good. We connect so well. In the beginning of our relationship I used to be very easy going about things and I didn't get jealous very easily. I was cool. For the past five/six months or so, I've been the opposite. I began stressing over everything!! Girls, him going out to the club, who he was texting, etc. I guess you can say that I've been a pain in the as*. I used to accuse him of cheating at least five/six times a week. I became very insecure in our relationship and I don't know why.
He's always treated me like an angel!! And I took it for granted. The times he used to go out and never cheat on me, I used to accuse him and start pointless fights and I guess he got sick of it. There's a quote that says "Never push a loyal person to the point where they no longer care about anything." It felt like our relationship was dying... I take most of the blame because I was too stubborn to realize that I had a great man willing to do anything for me and I just killed everything. I found out that he went to a party on Saturday and slept with another girl. He denied it for a couple days and then I confornted him with proof and I broke up with him.
He started balling his eyes out saying things like "I wanted to break up with you but I couldn't because I love you too much! I haven't been myself recently because my little sister just tried killing herself and now she's on suicide watch(this is true). He said things like "I'm so stupid babe you've been the girl that's stuck beside me through everything, you've always been there for me I'm so stupid! After getting accused of cheating for so long when I hadn't even done anything I felt like it had to happen. You pushed me into doing it." What are you guys thoughts on this? We broke up last night and then he called me and told me that he needs me so I went over for an hour and he held me for so long telling me how sorry he is how much he loves me. He said that everything happens for a reason and he thinks that this will make us stronger. He called me this morning asking me if I can see him later. I told him no. He message me earlier this evening saying "I just know that I'm sorry about everything and I really miss you." Almost every single time we've seen each other for the past five months, there would at least be two hours out of the time we were together that I was in a bad mood. I'd either accuse him, get mad at him for going on his phone, I wouldn't let him cuddle me for the dumbest reasons, etc. I don't know what to do!! I love him so much. Do I give him another chance?