Can I claim self-defense if someone attacks and provokes a fight and a fight but the person was hurt?

I’m in school. A kid walks up to me and said I stepped on his aur jordan 5's. I was in the middle of an apology when he then said that he will beat me. I told him that I don’t even know him and walked away. Then he got violent and said and pushed me so he drops his stuff as a sign of provoking a fight. I dropped mine. I took a swing and knock his tooth out and a tooth through his lip and knock him out as well. Can I claim self-defense and is there anything I can do about the school for not stopping the intercourse before it grew?