I’m sure it is worrying you. When someone is suicidal, confidentiality is no longer an option. I’m glad you tried to alert the school counselor.Your friend’s situation is beyond what you can expect yourself to handle.
What you can do is tell her for me that all therapists aren’t alike. I’m very, very sorry that she felt dismissed and minimized by the first therapist she went to. That should not have happened. But to give up on getting much needed help because of one bad encounter doesn’t make any sense. Most therapists will hear her story with compassion and will work with her to help her recover.
Tell her to please, give other therapists a chance. It may take interviewing a few before she finds someone with whom she feels so comfortable that she can do the work she needs to do to get out of her anxiety and despair.
A friend of mine once told me that finding the right therapist is like going shopping for a new pair of jeans. You might try on 4 or 5 pair before you find the one that fits just right. All relationships are like that. We try out many people before we decide who to trust. When you are older, you will probably try on a number of possible professions before you decide which one to study. Very few first loves become permanent. Most people try on a number of boyfriends or girlfriends until they find the special person they want to spend their life with. Finding the right therapist is no different.
Hold her hand while she makes another appointment if that helps her. But do take care of yourself. You are not responsible for her life. You can’t be. She needs to find the strength within herself to insist with her parents or her school counselor or another adult she trusts that they help her get the help she needs and deserves.
I wish you well.