Is 4 months good enough to reach out to ex ?

Me M19 and my ex F18 dated for almost 4 months and I messed up, this ended our relationship. I went over to her place and literally begged her to not leave. This relationship was very important to me as this was the first serious relationship for the both of us. When I went over to her place to ask her to stay, we ended up sleeping together. While I was leaving she said I love you “my name.” She told me that this does not have to be the complete end of us and when I feel like I have changed and worked on myself, I could reach out to her. For the next days after our break up we called eachother to remove pics from socials together and ended up saying Love you again. A week later I couldn’t keep myself anymore so I called her and she talked to me in the coldest voice ever, that really hurt. I ended up getting pissed and said a lot of crap as she said that talking to eachother within the next month or 2 is too early and there will be no meaning of our break up. For context how I messed up was by checking out one of her friend’s tik tok where her clevage can be seen which my gf at that time showed me herself and I tried looking up for it. Instead of saying sorry and showing regret and remorse for my action I got defensive and that was how I messed up. She said I was a disgusting person and had bad eye for women. Even after all these we still sayed we loved eachother while breaking up and slept together while breaking up. I really want to become a better person and reach out to her. I asked her if she would wait, she said let’s not hold eachother back. I asked her if she was trying to move on but she said that she doesn’t think she can even if she wants to. Her girl bff told one of my friend that she actually is trying to move on but I still think words might have changed when passing from person. I have exams ahead and I want to reach out to her again after the exam which would be almost 4 months after our break up. She said if I came back to her after changing we could talk again and go through the talking stage again. I really want to know if she will still have feelings for me or not after 4 months and will she actually talk to me or not. Is 4 months a good idea? How do I work on myself to become a better person?

Tl;DR I messed up badly but now I want to reach out to her again after 4 months and is that a good idea ?