I wonder how she would feel about changing schools.

It is rough to change schools and her very sensitive nature could make it even rougher for her.

I agree with Rive. about the value of individual support through counseling. Does she/could she see a counselor? I would have her screened for depression and social anxiety, which an outside-of-school counselor/therapist will do. I think that getting input from a counselor, and seeing if things get better through counseling, and taking into account how she feels about changing schools, would give valuable information to help decide whether or not changing schools would help her.

Would anyone at school, such as her guidance counselor, know her well enough to be helpful to speak with?

It can be really rough to see one's child struggle, my heart goes out to you.