Sorry to hear you're going through this.
Sounds like you've handled the break-up in a really mature way. It's amazing how sobriety lets us do things like that.
It's never easy to go through a break-up, even when you know it's "for the best" and whatnot. Knowing that it will get easier never helps much right now.
Hang in there and be kind to yourself. Try to get outside and get a little sunshine and fresh air if you can. And remember that you are AMAZING for going through this sober!!!!!