Can I win my ex girlfriend back?

So my girlfriend of 6 months dumped me 1 week ago. So we met in college I am a yr younger than her and she is going to be a senior next year at school. We met at school and immediately hit it off. We fell in love and shared very intimate conversations. We were both convinced that we had found the "one" and were gunna get married one day. Ik we moved very very fast. Anyways I met her parents we spent amazing time together and loved eachrher dearly. She was devastated when we left school and was so so sad. We committed to eachother that over the summer we would make it. She lives in NYC and I live about 6 hrs away. We texted constantly and face timed every night for the first week. We sent sexy pics back and forth to keep the intimacy up. I went down to visit 2 weeks after we left school and things were good. I wanted to kiss and touch more but she felt uncomfortable doing that in her house. I told her that I didn't think she would do anything for me once I got home through text. This upset her a lot and set a bad tone for about a week. I became kind of clingy and needy. Showing too much affection and attention and asking to FaceTime and stuff like that. This drove her away. Then I was rude to her about her comin up for a visit. She was gunna come but I was rude about her not buying the right bus ticket so she ended up not coming. This really upset her. A week later she told me she felt overwhelmed by the relationship and didn't know if we could do it cause we would have to go long distantce again in a year. We broke up soon after. She said she wasn't happy in the relationship and that she didn't want to do this again in a year. She met a lot of new friends this summer in NYC through her job. She has been hanging out with them a lot since the breakup. I wish I hadn't smothered her and overwhelmed her with all of this. So after the breakup I begged her pleaded with her and all that for about a day and got nothin. What should I do? Apology letter? NC? Next step?
Updates:
+1 y
So to update: she did contact me after the break up and asked if I was ok and how I was doing. I thought it was bullshitt and then we got into a long discussion about everything. She stated that she needed space and needed to be alone right now to work on herself. She said she doesn't know if we will get back together in the future although she said it isn't w yes or know answer. I asked her that straight up and have asked if there is another guy and she said no every time
+1 y
She said that deep down she thought we could work things out she just needed time and space to make herself happy. She said she wanted to make herself happy before making someone else happy. She said she needed to focus on herself her family and job. Her parents have been fighting a lot lately too so that is stressful for her as well. I haven't talked to her for about a week
Can I win my ex girlfriend back?
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