Seconding that. I don't have much to add, but a reminder to check yourself and make sure you can honestly be happy just being friends, or whether you're only really going to be happy if there's something more at the end of this. You have to assess whether you can be a friend, and whether she's actually someone you honestly want to be friends with. Former relationships can complicate attempts at going back to being friends, and may change your perspective on someone. Feelings are complicated like that.
But yeah, at the end of the day, you're the only one who knows your situation and her well enough to be able to make a judgement call here. I'm sorry it's hard; all the more reason to be cautious for your heart's sake. Just keep looking inside and being honest with yourself, and you can navigate through this.
Well, I'm officially done with my ex. No apology. No anything. Once you not only break up with me and then refuse to accept that I'm apologizing, and then go on to try to force one of my friends to date you, I'm done with you.
Not trying to be harsh here, but do be careful about apologizing to achieve an end; no one's obligated to respond the way you want them to just because you apologized. Whatever may have happened, apologizing doesn't erase responsibility or whatever damage was caused. It's fine to be angry. She may have rebounded to cover her hurt at the break up (it's generally hard on both sides), may have done it intentionally to hurt you in response to whatever happened, or may even have wanted to be with the other person from the start. Just like she doesn't have to forgive you, you don't have to forgive her either; it goes both ways, yeah?
I do wish you luck getting through this, though. It sounds rough.