Relationship Advice Anyone?

I barely have any girl friends. The only ones that I do have don't really have an opinion on this because they don't date frequently or at all, or just haven't been in a committed relationship. My boyfriend, S, and I have been together for 4 months and 8 days today. That's a big deal to me, considering I'm in Grade 10 and he's my first real boyfriend. Me and S were doing great. So great in fact that I lost my virginity to him 20 days into the relationship. But I had no regrets about it. Recently we've been fighting. A lot. We used to "bicker like an old married couple", all our friends would say. But we'd make up right away. A couple weeks ago he taught me how to throw a punch without hurting myself. He let me practice on his hands for a half hour or so. This was on a weekend that we went to my cabin with my mom. Tuesday after that weekend we went to school. At recess I was talking to my friends B, M, and J. We were all having a laugh. The guys are hilarious. S came over and we were best kind. Getting along, talking, laughing. I asked him to put his hand up so I could show B, M and J my failure of a punch. He did and I threw a punch at his hand. It lamely hit his hand. We all laughed at how weak I am. Then I started a conversation with just S, still next to the guys. Because of the conversation we were having, I started to playfully hit him. (Like I normally do. I used to get kind of out of control and hit him a little hard, then I'd stop, realizing what I was doing. But I completely stopped that before this day) On the arm, the chest, the stomach. With even less strength that I would put into my real punch. When I hit him lightly on the stomach he completely lost it. (He has anger issues, before he moved here he put a couple people in the hospital.. one of which was a girl in his gym cl). He double-punched me (used two hands) with a lot of force in the shoulders. My shoulders are very tiny, and very bony. (Besides, he's 6'1", 200 lbs and I'm 5' 3 3/4" and 112 lbs). I stumbled backwards and shrieked the most high-pitched, girly, bone-chilling, scary movie scream I have ever screamed. ("OOOOOOOOOOOOOOOOOWWWWWWWWWWWWWWWAAAAAA… Of course everyone who didn't notice ( J and everyone else but B, M and a few people who were right next to us didn't notice that he had hit me. ) I slapped him straight across the face with all of my strength ( Not very much.. but I tried. ) Everyone around us tried to cheer me up by joking about it ( But it just made it seem like no one cared about what had just happened ). I kept a stern face and crossed arms. I stared at the trophy case next to us. S put his arm behind my back, trying to comfort me, I didn't move but I had a very stiff, uncomfortable posture. When the bell rung for cl to start, he held on to the back of my shoulders, facing me and tried to kiss me. I ,obviously, tried to pull away, but he wouldn't let me. He tried to pull me in closer. I didn't want to be near him so I pinched his shoulder. He held me more firmly and kind of shook me to get my attention and said "A, you need to stop hitting me." In a soft, strong tone. I felt like everything was my fault. My next cl I went to the bathroom bawling. My friend K came in and I explained how much of a horrible girlfriend I am. And she helped me feel a bit better. When I got out of the bathroom, S was waiting for me outside, ( I had texted him letting him know that I was upset and he took that as a cue to come find me. ) he looked at me with sad eyes. I looked at him with my red, blotchy, tear-stained face and said "I'm gonna go back to cl.." When I walked into the clroom (it was right next to where we were standing) I jumped at an ear-deafening "BANG" I knew exactly what happened. He punched a locker. (the locker is bent in REALLY badly now) Anyways.. we made up, I don't know why or how but we did. But now we fight almost every day over stupid things. We don't bicker, we actually fight. Now, every time we fight I think about how he hit me that one time and wonder if he'll do it again, if I should break up with him. He says he's really sorry, he'll never do it again, he feels like ****, he completely regrets doing it. He said he felt just like his real dad (he was abusive towards S's mom, but is a better man today) and that he wasn't thinking when he did it. He bawled when I finally explained my feelings to him about the situation a week after it happened. He said he'd understand if I left him, but he wouldn't be able to live, he'd probably feel like killing himself. He apologized. But the fact that after it happened we fight more then ever and disagree on just about everything, makes me wonder if we should still be together. I love him with all of my heart, but I used to always say "If a guy ever hits me, I'm gone, right then and there" But after it actually happened I realize it's not as easy as it seems. My questions are: Would you leave him or try and stay with him? (He hasn't touched me in a harmfu