Hi. Thanks for your query, Coughing is a violent act of muscle action. Hence the muscles go into spasm and send pain to the back of the neck spine. The transmitted impulse cases sharp pain. I would advise you the following: Clinical evaluation and physical examination by an Orthopedic Surgeon. MRI of the cervical spine, muscles will confirm the diagnosis.. You need a proper medication comprising of an anti-inflammatory medicines with muscle relaxant action and painkiller properties. This is to break the vicious cycle of pain spasm pain spams giving more pain