Can I save my relationship?

I 18M recently got broken up with by my 18F girlfriend after a year. I moved in with her a couple months in.. (I know it’s fast but my life with my parents shattered) the start was great. Then I started treating her poorly about 5 months in. I wasn’t being a great boyfriend. I wouldn’t plan dates, write notes, etc. I basically just was not doing the things a boyfriend should have. She came to me and asked me to change and figure my shit out. I promised her that I would. This happened several times. Every time I would do better for a week then fall back into the funk. This went on till she broke up with me a week ago. Once we broke up I realized what I was doing and how bad I was being to her my life feels like it’s fallen apart because I do have a genuine deep love for her. She says we need to figure out how to be independent and be happy alone to be happy together. We are still living together as I have nowhere to go now. I move into an apartment 20 minutes away in 22 days. Is there any hope of us getting back together. I understand why she wouldn’t want to. I did the whole begging thing out of emotional desperation. I realized that’s going to push her away. She said she feels like me and her mom are forcing her to get back together and she wants it to be on her own time. How do I let that happen? What can I do for the next 22 days for it to go as smooth as it can. We don’t hate each other. There’s just some work to be done and some personal growth needed. What do I do to help this situation? She says she’s scared of getting hurt again and does not trust me. She says the desire is mostly gone. Can I fix these things? I’m lost and alone and figured this would be my best place to turn. TIA for any advice!