Welcome to the board of Health care Magic
As you have described well your condition. I' m able to make out that probably your cervical rib
is fractured. This only can be confirmed by undergoing urgent X-ray Cervical region ,which can be taken care by orthopedic surgeon.
Since your hands are cold
and sore. You must immediately report to emergency room to get the things worked out,to stop further damage to your nerve
Hope your query is answered.