I would have your child evaluated for primary, secondary, and tertiary adrenal insufficiency. Additionally, a full hormonal profile, including thyroid, is warranted. As I said in other posts, I don't subscribe to the notion of dysautonomia or, truly, any medical condition that ends with the word "syndrome." These conditions are simply nonexplanations for a variable set of symptoms that are physicians are incapable of attributing to an actual, verifiable medical problem.
As it relates to your child's symptoms, things such as anxiety, nausea, stomach pain, and rashes, are hallmarks of adrenal insufficiency. I say this because I suffer from adrenal insufficiency and had all of those symptoms and then some. Additionally, it's worth noting that I was originally misdiagnosed with POTS/Dysautonomia. Until you find an actual, verifiable cause of your child's symptoms, please do not accept those diagnoses.
It sounds a lot like a mast cell issue. My son was just diagnosed with MCAS and was diagnosed with POTS in 2009. His main issues are GI related. His started at age 10 and he is now 17.
Like your daughter he does not do well when he over heats, he even hates the sun shining on him through a car window. We just got his MCAS diagnosis on Monday.
My son's first diagnosis was abdominal migraines. He also gets itchy, but no rashes. If you scratch your fingernail down your daughters back, does it leave a red line? The doctor did this to my son and he got a dark red line that remained for a couple of minutes.
Christy