Is there anything that can cause pain to shoot trough the carotid artery in the neck to the head?

Nerve pain: Cannot imagine that pain goes through an artery, though nerves do travel in similar paths. Possibly a trapped nerve in your upper back is causing the shooting pain. Seek pain management advice, or neurology. My be that a steroid injection (seek a physician who is comfortable with neck injections - not all are) would help, or you may need surgery as a last resort. An MRI may be in your future..

Get checked: Could be carotidynia or a carotid artery dissection.