He should be evaluated by an ent physician. The cause of his phrenic nerve paralysis is also another component to understand. Cough can emanate from nasal/sinus problems, gerd, vocal cord issues, as well as pulmonary issues. Infectious problems and tumors are always something to consider. Swallowing difficulty from esophageal problems or diverticula formation alco could be contributing to his problems. Once evaluated, the need for further testing such as a radiological exam of the neck or sinuses can be determined and ordered. Best wishes.