I cried in front of my professor...what should I do?

This morning my friend told me that he cheated on an exam and had admitted it to the teacher due to his guilty conscience. Since he was looking off my paper, the professor believed that I was an accomplice when I really had no idea what he was doing. When I tried to explain that I was not involved, I started crying when the teacher did not believe me. It was important for me to convince her because the penalty for cheating is to be kicked out of the university..which I didn't deserve. Feelings of betrayal and disappointment overwhelmed me and I lost it. She ended up only penalizing my friend and letting me go....however I'm embarred at my behavior. Would it be appropriate to send an email and apologize for my behavior or just leave it alone since I was not penalized? Thanks...