cookfan,
You sound like a good parent ~ very involved and concerned about your daughter's well-being. It sounds wonderful to me! I agree with Maranara's advice and middle school wisdom. I also think that it's great that you are getting your daughter in to see a T.
I am curious if your daughter feels a bit overwhelmed by her school and after-school responsibilities. Does she still enjoy gymnastics? Is that a big enjoyment for her, or is she also trying to avoid that nowadays? Does your daughter have any pets, or a love for something tangible?
With summer approaching, you may want to see how she feels about spending some time volunteering in a community program. Like YMCA, elder care centers, library, cleaning up the park, etc. A lot of pleasure and fulfillment often comes with helping others in some way. It would also help your daughter meet others that care about the same types of things as she does, and make friends.
I am sure that it's very hard to see your daughter feeling so down. I was also a "loner" when I was in school years ago, and I strongly recall the misery that I felt. Try to remember that not all kids are the same. What works for one doesn't necessarily work for others. Your daughter is at a tough age. Talking with her teachers could definitely give you a better perspective to how she is feeling while she is in school. Does she ever smile and try to talk with others, or is she withdrawn and quiet?
I wish you the very best at trying to help your daughter through this tough time in her life.