Chris, The problem is that a neurologist is not an ENDOCRINOLOGIST!
An endocrinologist would understand that it is NOT common just because you have MG but is a sign of an autoimmune attack on the thyroid.
http://www.mayoclinic.com/health/thy...isease/AN00806
Do not expect your neurologist to know the details about endocrine issues. Please get a 2nd opinion, or rather a FIRST opinion, from a good endocrinologist. You will need to be followed closely.
Also, NatureThroid, the more "natural" alternative to Synthroid, is a good drug. If you are allergic to pork, however, you can't use it. Armour Thyroid is okay but they've had problems with both quality and availability.
I hope you will get answers you need soon!
Annie