Break up?

Hey guys. So I've been with my boyfriend for almost two years. There's been cheating and lying but things have been really good recently. Well today I found him calling some other girl baby, saying he missed her, and saying no one treats her like a princess more than him. I woke him up to confront him but he was basically out of it and just said she was stressed and he was trying to make her feel better. He has to wake up soon and I just don't know what to do at this point. I'm completely in love with this boy. I'm not weak minded. But breaking up with him is just going to cause me so much sadness and stress. I'm about to start working again and I have a really stressful job and school career as it is. Would you try to work things out for your own sake or break up with him?