What could be cause of jolts of pain down fingers when hand gets cold. Have recently had carpal tunnel surgery.?

Nerves waking up. It could be several things, but its not unusual to have a flare up of pain after cts as sensation returns. It can also be caused by scar, post-operative inflammation, and over use. Try ice and anti-inflammatories like Aleve (naproxen) or advil. If it persists, a short course of supervised therapy may help, including de-sensitization exercises like working your handa dn fingers in a pot of dried beans.
Depends. The symptoms you describe could be due to irritation of a peripheral nerve, such as the median nerve which is decompressed during carpal tunnel surgery, or a cervical nerve root. You should inform your doctor about your symptoms.