Carotidynia is a contorversial diagnosis and some specialists arue whether it exists as a seperate condition at all. It is also called 'facial migraine' - there is an acute form lasting 1-2 weeks and a chronic form thought to be realted to migraine and is treted with migraine medication. It is so rare that it is hard to study it and find more answers. The pain is thought to originate from the carotid artery . The carotid artery should be evaluated for other disorders such as an arterial tear, blockage or growth by MR etc. Carotidynia usually responds well to a course of steroids.
Good luck