It's me again. I also find cold helps my hands. It seems to distract the nerves and gives them something else to focus on. I run them under super cold water, or hold an ice pack for several minutes, when using for a while, like dart tournaments. It almost burns it is so cold. It seems to be the distraction I need for a bit.
If you are putting cold on your neck for relief. It may be your body temp is a bit high, while working, and cooling that area, cools the blood that is circulating the body.
If your doc is not satisfied and you are not either, good luck with more testing.