Was I right to leave?

Christmas Eve my bf of 4 years and I broke up. By the first week in January he was dating someone else all the while, begging me to come back to him and telling me I was the only one. I had no idea he was dating someone else. So I got back together with him and now 4 months later I discovered he has been texting someone named "Dan" quite often. (I can see the cell records because we work at the same company and his is a company phone.) Well "Dan" has been sending some strange messages for a while like smileys and that sort of thing. So it was no surprise when I found out "Dan" is actually a girl named Andrea. I confronted him and that's when he told me that he dated this girl during our two week breakup...all the while telling me he loved me, etc. Anyway, he claims the texts between him and her were platonic and just smalltalk and he knew it would hurt me if I knew about it so he put her under "Dan" and kept her a secret. Now he says he never told her that he was back together with me and that he is so sorry. He is grovelling and I do love him. Am I stupid to give him another chance? He says he never slept with her but I just don't know.