How to make up with my boyfriend? I'm desperate.

[loserguy]

People say things sometimes in the heat of the moment which they don't mean.
You have apologized and should not do so again.
It seems to me that you are insecure and he is playing on this - not good.
He seems to be reveling in this drama.
Sure, you could do all the things that I mentioned before but he needs to realize that exercising control over you is not good for you or him. It is unhealthy.
He doesn't want you to leave otherwise he would have said so.
No, he is playing a game and enjoying the drama.
I would confront him again as in how long more he is going to persist in this behaviour?
No answer in this case would be an answer.
If he refuses to communicate you should leave. Happiness is about being and trying to be happy, not living in misery.
However you mentioned that you are not prepared to leave. I think he knows this and he has you exactly where he wants you.
You didn't cheat, there was no breach of trust only things said in anger.
That shouldn't lead to the drama it has led to (unless this was not an isolated incident on your part?)

The way forward lies ahead of you - are you brave enough to take it?