Grandmac my dil also has Thallassaemia Trait. Oddly enough, it wasn't picked up until she was an adult when a GP in rural Scotland, of all places, suspected it.
She had quite a lot of symptoms at one point esp bad stomach pains for which no cause could be found. It is a few years ago now but I remember researching it and it seems that people,suspect there is a third group of 'sufferers' that has previously been unaccounted for, inbetween thallasaemia Major & Minor. They do not suffer the problems that Major people have but neither are they symptom-free.
I think she/you will need to be quite persistent in finding a health professional who will look at this issue with your dd, she sounds very unwell, poor thing.
My dil's condition became complicated by a dangerously overactive thyroid but now that has been sorted out and since the birth of a baby, her health in general has improved. I hope your dd feels better soon. 