Zuko, in the manner of teenagers, and particularly teenagers who have just undergone a massively stressful event that left physical marks, does not notice them not noticing and is convinced people are staring at him through all of his classes. He can't do anything to make the left side of his face less stare-worthy. He could take the ring off, but even in his current state of tension and self-conciousness he can recognize it's less conspicuous than the bandages, and he doesn't want to lose it. He tries swapping hands, putting it on his left instead of his right so he can put his whole hand in his pocket or under the desk and hide the ring that way, but he quickly realizes he doesn't like having the ring on his blind side and out of sight and switches it back. He doesn't do a very good job at paying attention in either of his first two classes.
He does look out the window at exactly the right (wrong?) time to see someone hitting someone else. His first impulse is to jump out the window. Thankfully, he does not follow this impulse, because even though there's no glass in the window, he is on the second floor. His second impulse is to lean out the window and yell, get someone's attention, but he doesn't know anything about this situation, or if anyone will respond, or really anything about what the consequences of 'getting someone's attention' will be here. So instead, Zuko keeps it simple, and runs towards the nearest stairwell, using his freshly-acquired and deeply mediocre awareness of the school layout to chart something like a path to the greenhouse. He's not entirely sure what he's going to do when he gets there, but he knows this isn't right, and he knows someone should do something. He should do something. He can't just watch that kind of thing happen and move on, and -
Ah. He's made it to the greenhouse. Not quite close enough to physically intervene, yet, but close enough that he can yell "Hey! What are you doing?" and expect to be heard.
Maybe that's not the wittiest or even smartest thing to say, but it's what comes out.