Hi I had my entire thyroid removed 2 days ago and i experienced the nausea also and I was told it was due to the anesthesia. My neck is still a little soar as if I have a crook in my neck and today I have been experiencing troubles swallowing. I thought after the surgery everything would be fine. So I'll take your advice and try it. I hope you feel better.
I can't really comment on the TMJ but I can definitely relate to the nausea. I had my thyroid removed 2 weeks ago and for the first 7 days afterwards I felt extremely nauseous. I would get dizzy if I tried to read or study and had absolutely no attention span. After about a week it all went away. I attributed it to the anesthesia and the pain meds they put me on in the hospital. Even though you probably don't feel like eating b/c of the nausea, force yourself to eat something. You probably have a tendency to keep your neck stiff, but again, make yourself move it around several times a day. Also, I noticed my neck felt less sore in the moring when I slept on a flat pillow (I had been propping myself up before). You'll really be amazed in a week or so about how much better you'll be feeling.