And it's even further from "I'm sorry for punching you in the face. I was wrong to do that."
Promising action to the contrary sounds a lot better.
Saying you're sorry you hurt someone, is you taking responsibility for something you did. Saying you're sorry someone got hurt, sounds like the victim was wrong for getting hurt, and it's the victim's responsibility.
I can only ask for your support to have the time to “show, not tell”; and in the meantime express my sorrow at having caused pain.
I will rewrite this for him.
"I can only ask for your support to have the time to "show, not tell"; and in the meantime I want to show you my sadness, regret for causing you feeling distress and uncomfortable."
I replace express and sorrow with definition coming straight out of a dictionary.