How do you reconnect with someone after mutual feelings got ruined by immaturity?

So basically me and this girl started as friends, then things slowly became romantic and emotionally confusing. We both clearly liked each other at some point, but communication was messy and awkward IRL. At one point she told me she didn’t think she actually loved me, so things kind of died out.

Months later we started talking again and the feelings honestly seemed to come back from both sides, but things became frustrating and immature between us. Eventually I got mad and publicly embarrassed her in front of some friends, which I genuinely regret. Since then we completely stopped talking.

The weird part is that even after all this time, there’s still this tension between us at school. We still make eye contact a lot, but we never actually interact anymore.

I’m not trying to act like I’m the only victim here because we both handled things badly in different ways, but I do think I crossed a line with the humiliation part and I understand why things broke after that.

Now I honestly don’t know what the mature move is:
Do I slowly try to rebuild normal interaction again, or is trying to reconnect after something like this usually a bad idea?

I’m mainly looking for outside perspectives from people who’ve experienced similar situations.