The most common cause of throbbing neck pain
on one side is Carotidynia . Carotidynia is a common neck pain
syndrome characterised by dull, throbbing, localized pain over the carotid artery bifurcation, but may radiate to the mandible (jaw), cheek, eye, or ear on one side .The causes are Carotid artery aneurysm ,Cranial arteritis , Infection , Carotid artery occlusion . Please go for an MRI or arteriography to rule out the condition .