Does my ex still want to be with me?

I am 22, and my ex girlfriend is 20. We were together for 18 months, but then I started to second guess the relationship because there was just something missing in our personalities. I think it was sense of humour and a lack of common interests. We were on and off for a couple of months, and she was really fighting for our relationship and wanted to be with me. Then I went overseas for a 2 month trip. We were still sort of seeing each other and sleeping with each other up until I left. During my trip we spoke occasionally. We went on a picnic a couple of weeks after I got back and things seemed really positive, although she said that she doesn't think we can be together for a while and it will be good to see other people. A couple of weeks later we spent the day with each other, then went back to hers and slept with each other. The following morning, she asked me if I had slept with anyone on my trip. I admitted that I had. She started crying and was really upset. Then she admitted to me that one night while I was away, she made out with her guy best friend and its happened regularly since and now its complicated because he really wants a relationship with her etc. He has been her best friend throughout our whole relationship but she said she never thought of him as anything more than a friend until recently, but he has always been there for her and they get along well. She has told me since that she doesn't find him physically attractive and has never thought of him sexually before. We have very very strong sexual chemistry though. We were on talking terms a week after all of this had come out and then over dinner she told me that she wants a few weeks to step back and not talk for a while to clear her mind. But she told me she wants me to fight for her. For the first couple of days after, she was even messaging and snap chatting me, then all of a sudden she became really distant and short with me. For instance, I messaged her to say that I can't stop thinking about me and after an hour she replied with 'I had a dream of you and that girl last night and couldn't get back to sleep'. During the 3 week break I dropped off her favourite desert to her house when she wasn't home. After a few weeks we went to breakfast and she told me that it wouldn't feel right for her to work things out with me. I was totally shocked and gut-wrenched. I never saw this coming because I've always had the power and thought that when I felt ready, we could work things out. I found myself almost begging eventually. She said that she's just scared that things would just go back to how they were at the end of our relationship after a few months, and that she doesn't know if she has feelings for her guy best friend. 2 days later I dropped off a 5 page letter saying how I'd never take her for granted again and that I want to go travelling with her spend our lives together. She sent a text the day after saying that working things out just wouldn't feel right and that we're not in the same headspace. It was very blunt, which she's never been before. Since then I haven't spoken to her for 3 weeks, but a few days ago she sent me a basketball game invite on Facebook messenger. I played a game a few hours later but that was it. Why is she doing this to me? And what is the best way for me to go about getting her back?