Girlfriend broke up with me and itts evident she has started seeing someone else. I need help?

[GJA]

She broke up with me and blamed it on one silly Facebook conversation. Unbelievable. It want the cleanest brake up and I didn't handle it the best way either because I was I love with her and got scared of losing her. As she was the first girl I truely fell for I guess I tried a lot to get her back although she said I could have done more to get her back. What did she expect me to beg or something? I got flowers, wrote her a card telling her how I felt about her and talked to her to try and work things out. What I can't get over is how quickly she moved on. Within a couple of weeks already on dates and now seeing someone else and keeping it a secret. I held on to false hope that we could work it out. I need to accept its over and I've taken the following steps. I have removed her from Facebook, just deactivated twitter account, signed up to dating sites just recently. But even when I talk to other girls I still think about her and honestly just don't want any other girl. Is this normal? Now that she is seeing someone else so soon is there any chance we could get back together? She sent me a Christmas card and I sent one back. Feel a bit silly doing so now but wanted to be polite. Please give me some useful and friendly advice, I'm torn here and really hurt still when she has just so quickly moved on.