I have pain on one side shooting down into my shoulder and back and am post RAI. I had some of the pain going into the RAI but never pre-TT. I'm not sure, but with mine, I think it boarders on pinched nerve almost and have been sleeping on a heating pad. I also think it's stress related more than thyoid related. Of course I didn't have a goiter, but cancer, so this is not really closely related, I guess. However, the surgery for anyone would be concerning enough to cause that kind of "stress-pain". Especially if you're like me and carry my stress in my shoulders and neck... Not sure if any of this helps, but the pain has been with me for more than two weeks and I was starting to get a little concerned, seems to be easing in the last two days though... I guess let down stress, in my case... Good luck with your surgery, let us know how it goes.
I do not know if the pain is normal but, I had TT on 11/16. Pryer to surgery I did experiance pain on the side that was affected. Since surgery, I have not been troubled with the same pain. If you do as well as I have post-op you will be fine. Keep the chin up and good luck