Hello Jessie's Mom,
You are on the right track. If you can get someone to test your daughter for Celiac OR gluten intolerance, this would be a very smart thing to do. See my home page for extra info in this regard.
I have found it to be VERY difficult to stay with traditional medical doctors when it comes to Hashimoto's and even Celiac. They simply don't have meds to treat these diseases, therefore, they tend to offer no real help. Finding a natural doctor, although sometimes a bit more expensive, normally offers great rewards as they guide you through natural treatments - which cannot be found in the traditional field.
Check out my last blog post about reversing Hashimoto's. You may be able to get some help there and get a consultation with my doctor or look up a doctor that can look at your daughter system wide. The problem with traditional medicine is that they see a body in all different "compartments" and the body just doesn't work that way. It makes so much sense to me now. If your car's battery goes out, there is not a good mechanic anywhere that does not also check the health of the alternator and charging system before making a definite diagnoses. The battery may be getting drained because of a weak alternator which is the thing that needs the most attention. Our bodies function in a similar way. This is why thyroid treatment with a pill alone fails miserably.
Gluten intolerance would be the next thing I would check. Also, if your daughter is a vegetarian (how long has she been one?), you may be dealing with some diet issues (low protein) in addition. A good doctor could pinpoint the problem through testing the different systems of the body.
Hope this helped. I hope your daughter feels better soon.
Mo
