Smoking; The degree of blockage in your carotid artery; Blockage of the carotid arteries on both sides of your neck; ... cannot control with the medicines you have been given; Severe headaches, swelling in your neck, or other new symptoms; Cough, shortness ... Carotid Endarterectomy ...he blockage increases your risk of stroke, a medical emergency that occurs when the blood supply to the brain is interrupted or seriously ... Treatment of carotid artery disease usually involves a combination of lifestyle changes, medication and sometimes surgery.