Does this look sincere?

Okay so two weeks fa I broke up withy bf of 3 months.
It was great for first couple weeks, although we lived far away we saw each other every giorno during three days of college a week.

But we drifted away as he became withdrawn from me for some reason... And soon started hanging out with his female friend more.

I got so stressed that in the end we arranged to break up and then he dropped me like a ton of bricks and acted like everything we had didn't mean shit to him.

Angry, hurt, and confused, I confided in some the other people in my class, detto a few things I shouldn't have.
I have been recitazione like a cagna towards the other girl da giving her looks and stuff (immature, I know.)
And now I just feel bad because he knows that I spoke behind his back. I realise after clearing my head that I should have been più mature about it.
But now I don't know what to do anymore. We haven't been on speaking terms since. I feel awful :(

It is very unlikely we will be ever getting back together o will be close friends, but I want to have the decency to admit that I was wrong.

Seeing as it would be too awkward to say this to him in person, should i Facebook him this? If so, when?
Thank te to whoever can help x