Okay, I have an older sister who will go to extreme lengths to avoid saying she's sorry, so I am speaking from experience this time. Me: "Srsly? Sis, It's TWO WORDS!"
If you are really sorry and if you're a true adult, I think you should bite your embarrassment (I assume that's what it is) and just apologize. Hey, it doesn't mean you have to be friends it doesn't mean you have to go through whatever you did again. and it doesn't mean you have to be on polite speaking terms for the rest of your life, either. It's the right thing. Sure, it will help you move on, but it will also give you peace of mind that you aced at least this portion of a difficult phase in your life.
But I guess it wouldn't be too bad if you don't... Maybe someone might assume you haven't grown from this experience. Not that you should particularly care what anyone other than yourself thinks... my head is beginning to hurt.