Mental illness is something that does run in families, so you are wise to take her to see a therapist and a psychiatrist. Try to find a board certified child psychiatrist. A neuropsychological evalaution may help you too, not becuse she has any educational deficts, but because relative weaknesses can cause some kids such anxiety, and knowing where they are may be very helpful. Say, if her fluid reasoning is weak in an average or high average range, but her cacluation skills are in a superior range, she may be angry at herself or frustrated with more coneptual math work, when the actual working of the problem came so easy. If she has even an average executive funciton, and poor impulse control or social reasoning skills, she may lose control, and cry or even say things in front of her peers that she later is able to see are clearly not good things to do and say, and so on.
You will want to have a full medical work up too, and be sure that there is no under lying illness or codition, like blood sugar issues, that could effect mood, just to rule them out as well.
There should be no stigma here for you at all. If she does turn out to have mental illness, contact NAMI in your area, they have wonderful care giver classes and are a great local resource. You will definetely feel less isloated because you will meet and know many other people who also deal with the same things you are.
Finally, take care of you. If she has a mood issue, you should be very dilligent with yourself, and if you feel like you need help yourself, get it right away. Primary caregivers, espeically mothers, are very commonly diagnosed with depression because of the stress of caring for a child with mental illness. I don't mean to scare you, but the teen years are a challege, and (for many people I know) just as you think you have it figured out, she will enter a new stage of development, and hormones kick in, and you hit another rough patch, and everything changes. Be ready for anything, and take excptional care of you.
M.