Cheating?

My boyfriend and I have been trying for a baby for what seems like forever now. Finally pregnant, about 5 weeks. I found texts in his phone to a girl about how he heard she's a great kisser and asking if she liked hung men, he also told her his name was John, which it's not. These texts happened 2 weeks before I saw them. When I asked about it, he said he immediately felt horrible about it once the conversion was over, nothing came of it and that it would never happen again.

I'm not sure what to do