Perhaps you need to talk to your parents and see if they back up your opinion on your personal looks. Then you need to have your parents talk to the school about the way you were abused.
Private or Public School there is no right for a faculty member to degrade and abuse you. Next time they call you a name of any kind or use degrading remarks to your appearance you need to be adult with them and tell them to stop. Then Explain to them that this is a professional establishment and they need to act like professional people, Not like a middle school child who feels the need to call names and degrade people for his own place in life.
The trick to getting away with anything now adays is to be more mature and outsmart the people who are making the rules. If you can pull off the fact that your acting more mature about the situation then they are the will automatically feel inferior and lose any standing ground they have. School or no School You also have to be prepared to give demands too. If they start calling you names or if they start degrading you. You have to be ready to walk out of their office and let them know that right away on the grounds that they need to be professional and have valid points, Not opinions. They need to come forth with what rules you have broken and stand on them like a professional not like a 12 year old. That is out right abuse if they make any degrading remarks about it. Legally they will also have to prove you have broken rules to kick you out of the school without risking legal prosecution. Then also can not demand you harm your person IE dying your hair again so soon after you have treated it. If there demands are harmful to you I think you need to seek legal advice and the advice of your parents over what they are doing.
Remember, Be and adult be professional. Even if you are only 14 having a breakdown is what they want to see. They know your going to be irrational and they want you to be.
Fsck the System, beat them at their own game.
Snakes? I just like to teraform!