Carotid Pain. Carotid artery pain is also called carotodynia. This is caused by inflammation of the arterial bulb, where the internal and external arteries divide from the common carotid artery. I recommend large doses of nsaids, such as Ibuprofen 800 mg three times / day for fourteen days. Prednisone is also generally very effective, but is used only if nsaids don't work. See your primary care healthcare provi.
Is it your carotid? How do you know it is your carotid artery. Does it pulse (throb?) I would not hesitate to get to a doctor asap. Get some personal answers.