Hello and thankyou for approaching DoctorSpring with your query.
I have gone through your case and understand your concern.
The pain you have described is suggestive of radiating neurological pain due to a pinched nerve. It can be due to a decompression in the neck vertebrae. It may not be carpal tunnel syndrome but the pain will be a similar nerve pain, just that it is pinched higher up in your neck and not in the carpal tunnel in your wrist.

In rare cases such a pain is due to a growth in the lungs or due to destruction of the neck vertebrae. Since your G.P has got an X-Ray (of your lungs) it rules out any such growth. You can get an X-Ray of your neck to rule out and degenerative changes in your vertebrae causing pinched nerve.

Treatment for such pain will be (1) analgesic tablets. You can take the OTC drug Ibuprofen 400 mg after food when required.
(2) Neck exercises. I would like to explain the exercises to you but they are better done under supervision. Hence I would advise you to visit a physiotherapist.

You can be rest assured this is not pain due to cancer. If the pain persists beyond a month, you will require to undergo evaluation.

I hope this has helped. Feel free to follow up.
Thankyou.

If the parathyroid was causing increase PTH levels in blood , it could result in loss of Calcium from the bone. This could lead on the bone degeneration - which can result in a pinched nereve. But since it is removed, you need not be worried about that.
Since you have had your chest X-Ray done 6 weeks back, and it was clear. It rules out any growth in the lung.

As I said earlier it is most likely due to a pinched nerve in your neck vertebrae.
You can take the OTC drug Ibuprofen and visit a physiotherapist for neck exercises.
If it persists for more than a month, you might need further evaluation.

Thank you