Communication is always the way to go by: Dawn Abraham
Good for you for asking for help in this situation. It shows that you are mature beyond your years.
What I have always found when I have a problem with someone, communication is always best. You may feel like you have already tried that but I am talking about real honest upfront letting your feelings out. I know this can be scary but it always works.
Approach your teacher like a mature adult not an angry child. Tell her you would like to talk to her and ask when is a good time. Make sure before you do this that you have prayed for at least a week that everything good that can happen in the world happens for her. Yes you heard me right. When you're angry at someone you have to let it go first. If you talk to her with a resentment she will since it and your words will come out angry. You want to come from a loving place.
Then tell her you are sorry for any misunderstanding between you and her daughter. Let her know that you genuinely want to make peace and ask her if she would like to start again. You feel you got off on the wrong foot and this school and your education is important to you and you would like to start fresh.
If you do this and mean it she will feel it and it will work. Make sure you do the work to let go of your anger before approaching her. Let me know how it goes.
I wish for you all the happiness and love the Universe has to offer! Dawn