Your reading into things WAY to much. You need to stop viewing everything as a potential sign and move on. Moving on doesn't mean the end, but it at least opens a new door instead of starring down that familiar path of heartbreak and loneliness. She jumped right into a rebound relationship, mark my words it will fall apart, its a matter of time.
For better or worse, you still had feelings which prevented you from doing the same. You need to take a deep breath and look around at what's out there. Shes 2000 miles away and you're in no position to try and rekindle a relationship through text messages, emails and phone calls.
I try not to speak in absolutes, so I wont say you can't fix this, but how could you take her back? She split from you when you started to miss her, regardless of your approach. She jumped into another guys arms immediately to fill the void she felt. Everyone is entitled to their own opinions and course of action. I was in your spot not terribly long ago and wallowed for a long time. The best thing anyone did for me was my dad giving me a hard talk. He didn't dance around the situation and didn't hide the facts. Its a lot easier to understand everything when someone paints the real picture.
You're probably questioning yourself and everything you did in the relationship...forget it. I have lots of questions left from my last relationship that I wanted answers. Eventually you realize that some questions are best left unanswered, both because there is no answer or it was never your fault to start with.
Leave it man, you have a girl somewhere in this world who wants you more than anyone else, she's not her.
---------------------------------------------------------
Edit: I got to thinking about your situation and it mirrors what happened to me last time around in a lot of ways. My ex ended up dating and moving in with the guy that had caused the problem in our relationship to start with. I never once contacted her after we split up for good, not once. She still texts, calls or emails me from time to time, she sent me a text recently asking me out to coffee. Maybe she misses me, maybe she wants to talk, maybe she wants to apologize, maybe her new relationship is falling apart, maybe shes pregnant, point is I don't know and I don't care. I have yet to respond to one of them and quiet possibly never will. I told her not a word from me until her new doormat was out of her life, yet now that I am past her, I honestly have no intention of talking to her ever again under any circumstances. You have to let the cloud of emotions fade before you will start thinking straight again, until then you will always lean towards her.
Its really ****ing hard to say good bye and let go of someone you loved and cared about, believe me its the last thing I ever wanted to do, but it had to happen. You really need to get out and be with people, socializing will take the sting off of things and help get you on level ground. You need to just cut contact with this girl no matter how you feel. She made a choice on her own to leave you, she then made a choice to throw herself at the next guy she saw. The ball is not in your court, nor is the real hardship here. Trust me, no matter how it looks from your end you are better off than she is in every way.
Get up, get out, get going, theres no pause button on life, you need to get yourself back out there. The sooner you make yourself uncomfortable, the sooner you will will forget and the sooner you will smile again. I did a lot of exercising to relieve stress, I am now in the best shape of my life...quiet a trade.
It could be worse, your 2000 miles away from the source. I work with the source.......AND her boyfriend. I rather enjoy it though, both of them duck there heads and can't muster the courage to even look me in the eye. Bow to no one, be proud of who you are