Is this worth it?

Okay well I go to the park pretty much everyday with my girlfriend, and notice this guy always picking on this certain kid. I mean that guy was maybe 18 or 19 years old picking on a 15 or 16 year old short kid. So I just let it go, since its not my problem. The next day i show up, there both there doing the exact same thing. I mean come on, why does the short kid even bother coming? So I let it go again. Only to have the bully guy sit in front of us and give my girlfriend a look i didnt like very much. At this point I was pretty ticked, but i let it go, I dont want to cause problems. He eventually leaves, and we continue to watch a baseball game til night. By the time were walking back to our car i see the kid that was getting bullied, and several other kids with bruised faces. I went up to them and asked what happened, but they didnt say anything and walked away. one of the kid was even bleeding all over his shirt. I tried to find someone in charge of the kids but didnt see anyone. I didnt bother to go to the park for a couple days and returned alone to get some volunteer forms, and see the same group of kids. But this time Ive caught the guy in the act of excessively bullying the kids. I mean if you saw what i see, then you would understand the anger that i was feeling right now. I confronted the bully and told him to please stop and leave them alone. But i get a extremly rude comment back calling my girlfriend a whore. At this point I hit him as hard as I can in his face. It didnt knock him down but I think i broke his nose. The fighting went on quite a while, with him missing alot, and me hitting him alot. until the little kid went between us stopping the fight abruptly but with no avail the bullyjust pushed him aside. Ive had enough at this point and just backed off. It didnt take long for the cops to arive and take me back home, giving me a lecture on how i should leave other peoples problems alone. Gave my parents a scare and left. Maybe i shouldnt have involved myself, but i just couldnt have someone insult my girlfriend like that. Do you guys think i did the right thing or should i just all together stay away from that section in the park from now on?

Sorry for the wall of text

Summing it up :

me and girlfriend go to park, bully picks on kid. Bully gives my girlfriend the look. Bully makes little kids bleed. BUlly caught in the act. I confront the bully. Bully insults my girlfriend. I beat him up. Little kid trys to stop. I back away. Cops come, and scare my parents.