If you are worried about starting your period at school, just take a tampon or pad with you. Your teacher isn't going to say anything to you haha, odds are she won't even know unless you tell her. If you do tell her, she'll just send you to the nurse so they can give you a pad/tampon and make sure you know what's going on. Your best bet to be discreet is to just carry a pad/tampon in your purse or backpack and if you think you start at school, simply ask to go to the bathroom or go inbetween classes and take care of it. There's no need to involve teachers or staff.
She's not your mother. You don't have to say anything. You will have symptoms before you start. It won't just happen all of a sudden. There's nothing to be scared of, you will see that you are worrying for nothing.
Don't worry you'll be fine.She'll understand unfortunately its one of those things we lady's have to go thru in life. Just make sure your prepare and carry pads with you.O and don't forget avoid anything white for now.