Need some advice, what is my ex girlfriend thinking, should i give up on her or not?

well when we got together we were both 17, after a month i was 18, and we went out for a total of 2 months. I liked her for a long time, and she is the nicest girl i have ever met, shes really pretty and innocent, and i was her first boyfriend. Since i was her first boyfriend i figured i'd take it slow, i didnt want to rush things and make her uncomfortable because i really cared about her, she couldnt kiss me in front of friends or people we didnt know, but i didnt really mind that. We had a few minor problems towards the 7 week mark, because i wanted to see her alone, and she wanted to do stuff in a group, and when i would try get close to her when we were in a group, since we only saw eachother like once a week, she would say i needed to ease up because it wasnt just about us. I was meant to see her with the group again one night, and me and he boys were at my house waiting for 45 minutes, and when i called her she said they were having a girls night, due to one of the girls having a rough time, but we got kind of angry that they had dogged us, so i called her and said well we've been having problems and i was willing to drive down and see her for a bit, but she told me to have a guys night and i got fed up and hung up, and apparently she got really pissed off at the fact i got angry. The next time i saw her she broke up with me, she said she didnt like me anymore, she felt differently because of what happened but i was the nicest and sweetest guy she had ever met, and still wanted me in her life, and told me not to leave so i stayed at her house and we talked for hours. Her friend told me she did it because i was too clingy, and that my ex didnt know if she had made the right descision, she was also crying when she broke up with me. I went to her house a few days later and tried to explain that i was still the same person she fell for and that i didnt mean to get how i did, i was just upset that i couldnt see her and i really wanted to fix things, but she said it couldnt happen, and was better off like this. I stopped talking to her after i tried to ask her how she was on FB and she just said good and went offline, but i saw her recently with the group and she was staring at me sometimes and was trying to talk to me. I just dont really know what to do, ive been told i deserve someone better who cares about me more, but i just liked her for so long so its hard for me to call the quits, i knew i was being too clingy, and asked her if she needed space but she said no, but then she dumped me, its hard for me to move on. Do you think that maybe just because she was pissed off at what happened she over-reacted, or maybe shes just scared about comittment because im her first boyfriend? i havent had a decent conversation with her for 3 weeks, i just need to know if i should try and get her back, or if its not worth it and move on, the most we did together was make out, but i still think we had something special, ive also decided to start going to the gym, and playing sport again, and we're both going to uni next week, will this work in my favour, as i knew i was being too clingy and was about to stop, and wouldnt do it again, and ill be more occupied this time