Dear E.:
You sound like a great mom because you are looking at the issue from many sides. When I was a child, I had similar symptoms. My parents took me to the doctor who said it was just anxiety. A year later, I was finally diagnosed with an ulcer. I had passed out from the pain a couple of times.
Just recently, I discovered that I have a gene defect that affects my immune system. It is a bit ironic, but I looking back, I can see that stress weakened my immune system which caused illness, which caused stress, and so on. Unfortunately, it took about 40 years to get a diagnosis.
Keep talking to your child and listening to her. Perhaps you can resolve the underlying cause of the anxiety issue, and if she has an illness, you will be able to get it diagnosed.
I did have anxiety, and for me, it was a vicious circle. I could tell that me family was exasperated and angry with me because I was always complaining and sick, so I wanted to be perfect so that they would love me. This made me even more anxious (and likely to get sick).
Keep loving her.
Jen