I have a specific spot on the back of my head that hurts when i cough what is this? its a sharp down lower toward the center of my neck on the right side. its not my neck

Cough headaches: are well known. Most of them are harmless. The actual cause is not well-established but may relate to pressure exerted in and around blood vessels in the area of the pain/scalp muscles. They usually spontaneously improve over time. Cough headaches which are longer lasting or associated with unsteadiness or dizziness could be related to a defect in the cerebellum and need prompt evaluation.

Trapezius: Your trapezius muscle runs well down your back and up into your neck. Because it makes up part of the musculature around your rib cage, it can get strained from coughing. This may cause you pain anywhere along the muscle including all the way up to where it inserts at the base of your skull in the back.