You already know you acted impulsively. I don't need to tell you that. Actually you both are acting impulsively. Both of you have had times where you disrespecting the relationship and each other. This is concerning to say the least. Sometimes the chaos of the relationship says something about whether the relationship has problems. That doesn't mean they aren't fixable. A reason to move on may be that another relationship may not be as intense and chaotic - this can burn a relationship out. Another relationship may not involve worrying if your girlfriend is dating someone else behind your back. It is great to come to your senses but that doesn't make it right. You would be able to develop a trusting relationship. What you did was childish but it wasn't dating another girl. You have to have trust in any relationship. So ask yourself is this possible with this girl. Everything can hinge on this question.
You need to look at this relationship realistically and decide if everything she has done is worth it. It is okay to want to be in a relationship that is not always positive but be honest with yourself about that. Trust is huge and if there can't be trust it is doomed. You can be hurt but not be naive. If you have to move on that comes with time and effort. There is no magic pill for a broken heart.
If this is helpful press accept