I got into a fight at my new school after someone said something about my sister. Did I handle it right?

I transferred a few weeks ago and have been trying to keep my head down and figure out where I fit. Then at lunch someone I barely know made a sexual comment about my sister in front of everyone, laughing about it like it was nothing. I shoved him. He swung. By the time a teacher got there it was already a real fight. Both sets of parents got called before the end of the day. My parents were furious. They understood why I reacted but that's not how we handle things. My dad said there were a hundred other ways I could have dealt with it. My sister found out that night and instead of being grateful she was embarrassed. She told me she didn't need me to fight her battles and that now people were going to be talking about it and making it worse. I'm the only one who seems to think I did the right thing. I started thinking about why everyone's reaction had caught me so off guard. I'd been so focused on what he said that I hadn't thought for a second about what came after. I also thought about what I was actually trying to accomplish when I stood up. Was it about protecting my sister or was it about me and how it made me feel to hear someone say that. Those felt like the same thing in the moment but sitting with it they weren't exactly the same. I realized that even if my instinct was right the execution put everyone I cared about in a harder position. My sister didn't feel protected. She felt exposed. My parents weren't questioning my values they were questioning my judgment. And I was at a new school with no allies and a situation I had no idea how to navigate. Talking it through helped me realize I'd been so caught up in being right that I hadn't stopped to think about how it landed for everyone else. We agreed on two next steps. First go to my sister and just ask how she was actually feeling. Not to explain myself or get her to see my side. Just to apologize for making things harder for her without meaning to. Second go back to my parents and actually ask them what they thought I should have done differently and how I should handle things at school goimg forward.