I found texts on my H phone when I was 7 months pregnant. I had made him a special birthday dinner that he didn't even come home for, then he came home late and drunk off his ass, and passed out on the couch. He had sent his boss a lot of sexual texts while he was at the bar with her, even asking about having sex.
He still says he doesn't remember, but I have a hard time believing he would wake up & delete texts & still be in a black out.
My DD in 2 weeks old now & we're talking through our problems still. We had started MC, but I said no more until he does IC to examine possible sex addiction. I've been going to my own IC and started immediately after DDay, which I would strongly recommend you do. I've talked with friends and my H's step mom about him cheating, but there's so much more you can tell a counselor without having to filter anything.
It's really important that you take care of yourself first right now. Writing everything out can go a long way for organizing your thoughts. My head has been an absolute mess trying to handle everything on top of the already physical & emotional strain of having a baby. If you can't talk to him, write him a letter.
I'm so sorry you're going through this. He's robbing you of what should be a special and exciting time. Do whatever you can to take that time back for yourself, your baby, and your DD. Whether you work things out or not with your H, he is truly missing out on this time and will regret it.