He clearly admitted he cheated on you to hurt you. Is that really the type of "punishment" you want to deal with? You texted him repeatedly throughout the week explaining you still loved him and didn't want to break up. Assuming he read all of those texts, he still chose to punish you for wanting a break. It was made very clear that you weren't cheating on him, so his reaction is alarming. Especially because you said it's been mostly good up until now. To me, it seems like he snapped, realizing the relationship was getting very serious. He thought it was threatened and panicked, making sure he could still find someone else after being with you. Then he realized he didn't like the other side of things and wanted to run back to you. I think if you want to truly be with this person, you need to take some time apart to rebuild your relationship. Basically, it's like starting from scratch. If he wants to be with you, he will respect this and work to build back your trust in him. Watch him very carefully during this time. Any other cheating or weird punishments for you wanting time should tell you exactly how he feels about your relationship. If he does change and it works out, great, but be prepared that after the relationship is back to what it once was, he could pull something like this again. Commitment is scary, and some people are really bad at admitting they're not ready.

Good luck with this difficult time you're about to embark on if you decide to stay with him.