Authorities will always immediately quell any currently-happening hostilities when they arrive on the scene, that's a clearly necessary first step in order to figure out what the hell is happening. A common bullying tactic is to bait the person into fighting back, knowing that the anger will push them so far they get in trouble.

You see, the bully has enormous amounts of experience and practice at toe-ing this precise line. The quiet kid does not, they're quiet, they don't run into it very often. The bully knows this.

So, if you absolutely must hit back because nobody and nothing else is helping, do it quickly, decisively and cleanly, and then stop. Re-arrest your own feelings, and go back to calm. You probably will still get in trouble, but the other kid is more likely to get in trouble with you. And you're less likely to do medically significant damage anyway, if you just hit once instead of wailing on the bully for a solid minute, so, that's better for everyone. If you actually really hurt the kid by accident, that's a whole different ball game, you don't really want that. You just want them to stop doing this in the future, that is all. Deterrence for the future is different from revenge. Revenge is impractical because of how extreme it is, it can create feuds, make things worse. He can avenge your revenge, if you are too harsh. But simple deterrence is a different story, when you're not too harsh, and instead using just enough force to get the safety that you want.