What should I do about my relationship problems?

Ive been dating my boyfriend for a little over a year now, and a few months back, he broke up with me because he said he wasn't sure about us anymore since we are both each other's first official relationship. The next morning, I found out that he was already talking to girls on tinder when he told me that we were only going to take a break to give him time to think. I gave him an earful about that, but we ended up getting back together. The next month, we were afraid that I had gotten pregnant and he panicked and was messaging girls over social media again when he was drunk one night, but it wasn't girls he knew so I ended up forgiving him after we fought about it, and we stayed together. About four months passed, and just last week he told me that he went out for coffee with a girl from one of his classes but said it was nothing more than just friends. I believed him but was still suspicious, so when he was at my apartment this weekend, I checked his phone and read the messages between him and her. They were very flirtatious and he even told her she was cute. After they went out that day, he sent her another text that said "I'm sorry that I didn't tell you this earlier, but I have a girlfriend and thought you should know." She said she was also seeing someone so she was glad to just be friends but then never responded to him again. He tried to send her a text a few days later but she didn't answer. They were also snap chatting but since those disappear, I don't know what had been sent back and forth. She stopped answering those, too, though. It seems to me that he was interested in her and making it obvious to her. I confronted him about it and he apologized and said that he just blanked when she was being flirtatious with him and that he later realized it was wrong and came clean to her and me about it, and he said that he didn't tell me the flirtatious part because he didn't want to upset me since it was a mistake and he wasn't going to do it again. I almost broke up with him that night and the next day, and he was crying and told me I should because I've never done anything but be good to him and I don't deserve to be with someone that would treat me like this. I decided to give him another chance, and he promised that he would do whatever he could to earn back my trust and promised that I deserve nothing but the best so he will become that for me. He also told me that recently, he had been going on omegle video chat and jerking it to random girls; he said he told me because he didn't want to hide anything else. He also has a lot of personal problems stemming from his messed up childhood, and he would always go online and talk to girls to escape from that. That was just a way that he coped with it, so I'm trying to be understanding but also know that I don't deserve to be hurt like this. It's not my obligation to put up with this and I'm just at a loss for what to do. He told me he'd do anything I wanted him to do and that by going on this date he realized that I'm the only person he knows that will always be there and truly accept him and he will do whatever it takes not to lose that. I know this could be a load of crap but I decided to try again. I'm just confused, though, because I know that I'll probably be saving myself from future pain if I just dump him now, but that's not what I want. I just need second opinions from people that don't know me or him. Thank you!!!