Second chance after Emotional cheating?

Sareni

*LONG*

This week I found out my boyfriend of 8 months has been emotionally cheating on me with an ex since we got together. I had been suspicious of him for months because he was always so protective of his phone and secretive. I asked him why several times and he would just get upset about it and say that his exes always demanded to see his phone and he was paranoid. So I let the topic go and gave him his privacy. But then this week I couldn’t handle it anymore and I went on his computer and read some old messages on his social media between him and his ex. I found out that they were taking a break and that he was “working on himself” to get back together with her. They talked about how much they missed one another and how they were going to be together once he transfer to her school in the fall. I honestly couldn’t believe it. I confronted him about it and he apologize. He said that he didn’t know why he did it and that he doesn’t want her anymore, that he wanted me. After many arguments and crying from my part, I decided to give him a second chance. But now I think I made a mistake because he is clearly not over his ex and he still has feelings towards her. I also can’t trust him anymore because he had been lying to me the whole time we have been together. I even told him to stop talking to the girl and to tell her about the relationship we had this whole time. He was really against it, saying that I was forcing him to do something that he didn’t want to do and that all I wanted was a power trip from this. But that wasn’t the case at all. All I wanted was for him to get closure from his ex and to not have me as a second option. He eventually did it but he still upset about it. Did I do the right thing by giving him a second chance?