Well you can ask her from the outset about the limits of her confidentiality. She may have some personal policies but, especially if you're a minor, she will have legal protocols to follow.

She would most likely need to tell someone else if you tell her you're actively suicidal. That might be what needs to happen in order for you to get the help you need. It's probably a good idea to tell her. It might feel uncomfortable and she might need to involve your parents and maybe a psychiatrist or another healthcare provider. It won't be a picnic. But it sounds like you're not having such a great time anyway. Give yourself a chance. It's amazing what can happen when depression gets treated.