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..