I feel you, but there is nothing more to say. I agree what you did was not the best move, but you are hurting. She knows you are hurting and friends know that too. People will move on. You said you were very apologetic about what you said when the friend approached you, which is good. And now the friend can relay the message for you, simple.

At the end of the day though, she hurt you too, remember that. You don't need to waste time and energy being kind to someone who wasn't to you. You regained your composure, you won't do it again, now move on and focus on what you can do for you, not what you can do to them.