How can I sue my school?

I don't believe you and think that this is a troll, but I'll answer just for fun.

You have no valid claim of racial discrimination because there is absolutely no indication that any actions by the school were racially motivated. Being black does not shield you from the consequences of your actions. You were disruptive, sexist, hostile, and violated multiple school rules and policies regarding student conduct. They would have been within their rights to expel you, so a 3-day suspension is going easy on you.
Meanwhile, defamation requires that the school make a statement about you that is untrue which they KNOW to be untrue which was done maliciously AND caused irreparable harm to your reputation resulting in financial harm. As near as I can tell, you lack every single element for defamation.
Next time you go back to school, try listening to the teachers and you might just learn something. This will save us all the time and trouble of educating you here.

I knew Johnny Cochran. We attended the same schools. at different times. If he were alive today reading your letter he would be indignant and outraged by your pettiness, juvenile behavior and unbecoming conduct.

If you do not believe me, I invite you to call his law firm and inquire how they would feel about accepting your case.

If the school was over reactive, and I find no evidence of that, you are over reaching by connecting blatantly abhorrent, inexcusable behavior combined with the poorest of judgment
and seeking to wrap your embarrassing conduct into the fabric of a civil rights violation? I think even a man of peace as Martin Luther King would want to minimally box your ears and demand you behave, learn and educate yourself in a proud manner. You have well made the case for your ignorance. Thankfully you will have time to make-up for it and become a leader of people. Leaders neither mock, embarrass nor strike out at others....but you know this already.
Follow the proper path and this case will bring you an eventual victory for personal development and social benefit.

HAHAHAHAHAHA no. Sorry hun but you are in the wrong. Defamation is saying something that is NOT TRUE. They said nothing that you did not say. Racism? OMG that is getting to be old. Getting beat up because your BLACK is racism. Being lynched because your black is racism. Please learn what REAL racism is. Not telling you off because your being an ***. She did not say "Get out of my class you n word". In fact you where being sexist with your "get back in the kitchen" remark. GROW UP.

Next time keep your mouth shut and you won't have this issue. Go a head a play the race card and see how far that will take you.

No it won't, because the judge and jury will hear what you said to the the teacher and just laugh in your faces.

You are a pig! How dare you speak to anyone in that manner.

No-one will take your case seriously. Grow up and learn your lesson.

No, no one will take you seriously because you are at fault.You should grow up and and start thinking in a more matured way.