My daughter was 13 when she had similar symptoms; we went to the "best" specialists around - one asthma/allergy MD, three pediatric GI physicians, two OB-GYNs. Four different hospital systems. countless tests and surgeries. It took four years, but we finally found an MD that diagnosed her correctly. Go to a holistic MD for a thorough exam. We found it that the culprit was a CASEIN allergy - not lactose- casein. Her antibodies were off the charts. Once we removed anything dairy or processed (because casein is in everything processed) she had quick relief. I never thought much of holisitic practitioners until we experienced it firsthand.
Good luck - don't give up.
Thyroid replacement hormone, Such as Synthroid, can affect adrenal function and cause nausea, vomiting, fatigue, abdominal pain and other symptoms. She made need to take Hydrocortisone now, to balance with the Synthroid.
She should have a thorough work-up done by her endocrinologist to examine adrenal function.
In the meantime, you can try ginger tea, or slippery elm, to help with nausea and stomach upset. She may need sodium, if her adrenal function is suppressed. Offer her a tiny bit of salt, when she feels nauseous, or baking soda, and see if it helps.
When she does manage to eat, taking digestive enzymes with her food could eventually help a lot. I highly recommend digestive enzymes.
Enzy