Is there still a chance (please help)

My boyfriend and I are having a lot of problems and they started in December Of 2014. At that time we had been dating for maybe 2 months and I broke his trust. I hung out with another guy and lied to him about it. The guy was also flirting with me and I flirted back so I understand why he believed more than that happened. When we broke up we didn't talk for a week. After that we began seeing each other, sleeping together, but not officially together because he didn't trust me. A few months later he got a new girl friend and we tried to be friends. That lasted for maybe a week and we have such passion for each other that he cheated on her for almost 3 months with me (their entire relationship. During this time I was seeing other people and yes having sex with other people one of them being the guy he originally thought I cheated with and I never told him. He found out and was broken hearted that I never told him but he was still in love with me but did not trust me. Around July 4th of 2015 he broke up with his girlfriend to be with me. A few days after the break up he realized he missed her. From this point he went back and forth for months. Not knowing what or who he wanted. Being in love with me and not trusting me but also caring and loving her but not having as strong as a connection as ours. We tried to end things multiple times but we always found out way back to each other. There was a lot of fightin and craziness involved with all 3 of us . Recently about 3 weeks ago he decided I was the one he truly wanted although he had feelings for her, his feelings for me were stonger. About a few days into out relationship there was a death in his family and he took me home with him. I met his whole family (first girl he has ever taken home) they seemed to have really liked me. While we were down there we fought occasionally mostly over small things like food orders or me not listening to him enough. His ex was still in contact with him while we were down there which put me on edge even though he told her her was with me. I left a week before him so he could have alone time with his family and she texted him again. She began telling him things about my past, guys she thought I had been with and things like that and he believed her. He started to say that the way we were when we went to visit his home didn't feel like he wanted it to and that it didn't feel how he thinks love should feel. I tried to get him to wait until he retune home but he insisted on ending things and was being pretty mean because he was so upset about all the things she kept telling him. I got annoyed and wrote her a letter about all the cheating and lying he had done and showed her messages that he had sent me and she left him. At the time of me doing it I knew it would infuriate him and he would be done with me and he was. He told me he still loves me and always will but he doesn't want me because I'm "crazy" and this isn't the first time I lashed out like this. I still want him back. Do you think I still have a chance with him? He has been the only person I have been with for the last year. Everything she was telling him happened 2 years ago but I didn't do the things she said I did which is trying to sleep with other guys. They were my friends but he doesn't believe that.

I suppose neither of us trust each other and I want to end this 3 war relationship and I know we love each other were just young I'm 21 so is he and the other woman is 28. He says he still loves me and always will but he doesn't want to be with me anymore because I'm too crazy and we fight too often

Life is only going to get more complicated and harder as you get older. There are a lot of guys out there who you wouldn't have to fight for their attention. That being said you have to be willing to give them your undivided attention. I would suggest breaking all contact with him for a month and I mean all. No social Media stalking, no replying to his messages. You are young and deserve time to yourself, minus all the drama to discover who you are and what you want. How you want to be treated. This is all you know and there is so much better to get to know. All this pain and drama is like an addiction you have to break. I promise once you do you will see a whole bright world out there. If A guy can't commit to you, which he hasnt, sounds like he is playing both of you, he isn't your long term love. You also have to have the maturity and self esteem to be faithful to someone as well:) and you are not crazy!