What happens if he thinks you're cheating on him in the future?
Whilst it was totally wrong for you to go out with the person you cheated with, choking you and hitting you on the face are signs of his inability to control himself.
He could have decided to end the relationship because you went out with the person who you should have been no contact with after the affair (whether individually or as part of a group) instead of resorting to violence.
He could have killed you in his rage even if he didn't intend to. What if you fell and banged your head.
I think this is a clear case of the mistrust that is forever present once infidelity has occurred. He isn't over it and he probably never will be. Getting married would be a disaster and a divorce down the line.
From his side you shouldn't get married because:
● he doesn't trust you
From your side,.you shouldn't get married because:
● He's been physically abusive/violent
People shouldn't get married with no trust and with a violent partner.
There's no excuse for such violence.
Has he ever been violent before?