Please answer: Am I right, or wrong about this?

That's not really enough information to determine who's "right," but it sounds like she cares about you. I'm not saying she didn't do anything wrong, I'm not sure what it is that she's done (or not done) that makes you feel like she doesn't have your back. But do notice that this is now two people in your life you have drama with. Drama is on both ends, and if you don't take a look at yours, it won't get any better. As for the physical fight, if it was just self-defense on your part, you didn't do anything wrong. But from the sounds of it, there was a lot of build-up, and build-up can almost always be either managed or avoided altogether. You don't need to go apologize to the girl who started the fight, but you need to have the humility to admit your role in the situation. There's nothing wrong with being wrong. It's a rare situation that someone was 100% the victim and not at least a little bit of the problem. Don't make this about her, make it about you, and use your judgement. You probably know deep down if she's a good friend or not.