I am so sorry your DD is going through all of this, how tough for both of you
. It sounds like she has a lot going on mentally and emotionally and it's all just spilling out, quite possibly the result of one little thing that was her breaking point. Keep talking to her, asking questions, letting her know you love her, and taking pressure off where you can. Anyway you can get her in bed earlier on gym nights?
It wouldn't hurt to talk with her teacher and a school counselor, get some feedback about what is happening in school. And they could possibly give her some helpful tools for dealing with stress and expectations, things that will serve her well, especially if she is a high intensity child.
Dig more into the issues at school, feeling bullied, alone, or missing out on peer groups can be a big deal to kids. Are the kids in her group at the gym about her age? Is there one kid she really connects well with? Maybe making a point of encouraging that relationship and helping her build connections within her team could help her confidence.
Have you tried asking her what would make her feel better? Time off? A day for just play/fun? Ice cream date? I know you probably have asked that, but maybe getting her to think about what would help could give some hints as to the root of the problem.
I really wish I could offer more help, I was a very high intensity child and worked myself up about everything from a pretty young age, so I really feel for you and your DD! Keep us posted!