I have the same problem! I tried Levothroxine - switched to Synthroid brand, and my neck is killing me. It's the vertebrae area that hurts. I can't get it to stop - even with tylenol or pain killer. When I quit taking it, for a month, it stopped, but doctor says I need to take Thryoid meds.
Not a common side effect -- talk to your doctor about the neck pain.