I [23M] apologized to my ex-situationship

We were dating each other for about 5 months, and things were great except for the fact that I was being unsure and avoidant. We talked about it together and I made it clear that I didn’t know why I was feeling like this and that there was something wrong with me and not her. Eventually after 3-4 months, I told her that I don’t feel like I’m ready for a relationship but I still want to see her, to which she agreed. During this time, I started to pull away from intimacy because I didn’t want us to have a false sense of connection that I believe should be reserved for couples. At the end, she told me that she thought it was best for us to stop talking because we weren’t on the same page anymore and I agreed with her.

It’s been 3 months since then and I realised that during the past 3 months, I’ve been avoiding processing my feelings for her by being busy with work, exercising multiple hours a day and hanging out with my friends and family. When I finally got some alone time, I realised how badly I messed up. All of my friends said it was my fault and I didn’t have the right to ask for a second chance, except for my mom. My mom think it was all my fault but she said that because we were cordial and kind to each other, it won’t hurt to reach out to her, to apologize and to ask for a second chance.

So i decided to sent her a text, taking accountability for the things I did wrong and looking to see if we can reconnect again. Am I wrong for this?