Apologizing isn't as hard as you think. Most of the time, the other person is ready to do the same. They might lack the courage to be so humble. So be brave, step up, and say "I'm sorry."
You just might be surprised at how easy it will be.
And if you still lack courage, seek it in Confession, which is a fine way to first find forgiveness for your anger, and then gain the graces necessary to be as humble as you must be to apologize without excuses or justifications for your actions.
Be not afraid.