Right now you need to let go of the outcome and focus on making yourself a safe partner (for your BBF or someome else).
Confessing was a good first step, but he may need some space to put his life with you into his new perspective. Or this could be a dealbreaker for him.
Work on you, let him know you are available if he has any questions, tell the truth if he asks, apologize,
I was blindsided by FWH's confession but after the initial shock wore off, things began to make sense. It took awhile to adjust.
I can only control myself, no one else. I do not have that kind of power.
I didn't see you mention if you were in IC. If not I would recommend that you start. Find one that deals with infedelity and stick with it until you can dig down deep and find out the reasons for cheating and any other FOO issues you may be dealing with that may have contributed to your A or other issues you may be having.
As far as knowing if you can R with your boyfriend after this only time will tell. It may be a deal breaker for him. R is hard when you are married, but I would think it would be even more so if you are not and have no children to consider. I do not say this to discourage you, only to point out that it is a long hard road to go down, not only for him, but also for you. Sometimes as you know love is not always enough to get past the betrayal of infedelity for the wayward or the betrayed.
What you need to do now is show you want to R with actions, not just words. Words at this point mean nothing. You have to really own this, not just for him, but for yourself. (((HUGS)))