When my daughter was 13 she fell ill with anxiety and OCD. Like your daughter, my daughter shared information with her closest friends from her sporting club and the reaction was unhelpful.
I know how hard it is for you to watch this playout, feeling powerless. I felt the same. It is heartbreaking and the urge to protect is strong.
Unfortunately, 13 is a very young age for someone with no lived experience to really understand mental health conditions. I have met many adults who still don't get it and some that never will.
My daughter chose not to tell her school friends and relied on me, other family and her psychologist for support. Fortunately she had an older cousin she could talk to and the cousin took her under her wing. My daughter had many friends throughout high school, she just chose not to talk to them about her mental health.
My daughter found it much easier to talk to her friends and gain peer support after she graduated (she is now 21). The intetesting thing was that, a lot of the girls she had gone through high school with had also experienced their own mental health issues. Stigma, lack of maturity and a lack of knowledge simply got in the way.
I'm not sure if I'm actually helping you but just wanted you to know you are not alone. It's really tough. Hang in there.
Kind thoughts to you