I want my ex girlfriend back so badly it's killing me.

We broke up after a year and a half of being together because I felt I was changing (becoming 18) I thought I wanted to move away and start a new life, and that a young boy doesn't need anyone. I still loved her but had never been single before her (we were virgins when we met) and had never experienced the whole being a single young guy thing before, I thought that's maybe what I wanted at the time because all my friends are and they seemed really happy, but after breaking up and a few drunken kisses in clubs I completely realised how stupid I was (I am yet to have sex with anyone else, nor is she, and I don't want to anymore). At the time my parents were breaking up and I had this destructive I dont give a shit attitude but in reality I loved her. We were apart for 10 weeks and we both still loved eachother and spoke a lot but I was scared to get back with her as I didn't want to hurt her ever again. I realised being without her is not what I wanted at all and I could never hurt her again. I found out she was heartbroken for atleast 2 months after we broke up so I thought I might still have a shot when I finally attempted to get back with her she said that 'everything happens for a reason' she knew who I kissed after we broke up and it really hurt her and felt as if I didn't care about her at all. The attempt was quite out of the blue (stupid but i panicked) involved calling her explaining, she cried because deep down I think she still has feelings for me (we are each others first love) but is too scarred to go back. So I wrote her a letter the next day (about a month ago) trying to describe everything and how much I ****ed up and she's my world. She said that it's not what she wants and she doesn't want to be heartbroken all over again, so I left it there and gave her space for a few weeks. She knows I still love her so the whole friend thing will probably not work out but over the past month I have been improving myself significantly, keeping positive on social media etc and I've seen her once but I probably came off overly nice in hope that she'd see the light. We have texted a couple of times but she is being a lot blunter than usual. I don't want any advice to 'learn' and move on and that i'm young because I know all of that and have learned so much but I refuse to give up on this i'm completely in love. I just want to know do I fight so hard for her, show her how much i'm hurting and make her feel my love because it's my fault we broke up and she has just lost trust/she's wounded by it (but scared i'll push her away), or do I distance myself and try to start again as friends? We live in a town and same age so no doubt I'll bump into her over the next month, do I play it completely cool or try to make her feel special? I feel like i'm running out of time and that after December i'll have lost her forever. I know it doesn't have to be over. I beat myself up every single day with regret and privately cry for hours, firstly with stuff I never said or did, and secondly with why why why I ever destroyed something so innocent and perfect. I'm starting to get scared that she'll finally get completely over me soon and so I want to do something about it straight away even though I know I need patience and to give her time. It's on my mind every single second, even when I sleep, it's eating me alive and I can't concentrate on anything. Please only offer advice about ways to get her back I can't deal with anything else right now, Thanks.

If you cant be bothered to read everything above:

This Is how I feel - (Jeff Buckley) Lover You SHould've come over
I think this is how she feels - (The Japanese House) Still