First, re: giftedness testing. Is there any chance you can take her for testing using your medical insurance? Being outside of the educational setting might help her performance. Also, from what I've read on here and Hoagie's Gifted, using a psychologist who specializes in working with gifted children might help bring out her best.
I think there are definitely signs of depression in the symptoms listed....somatic complaints, etc. However, I strongly lean towards trying natural wellness before using medical interventions (having had horrid medical experiences in my life). So, I would recommend finding a good chiropractor who has a good background in nutrition. There are good natural preventative/restorative measures to take....i.e. using omega 3 and 6 fatty acids, making diet changes such as the diet Laura Gray used with her kids, vitamin intake, excercise routines...etc.
Also, find a cognitive therapist if you decide to go the therapy route. That will help her identify self-defeating patterns and reduce their impact.
Then, the giftedness needs to be addressed. Is there a gifted support group in your area? Perhaps you can join up with one of those to help her find people like herself. They don't have to be her friends, just meeting them and seeing that other people are like her will help.
