I have not had that on bp meds but have only taken them since December My friend does have this dry cough from their medication. Are you on an ACE inhibitor? https://www.webmd.com/hypertension-high-blood-pressure/guide/side-effects-high-blood-pressure-medications https://www.webmd.com/heart-disease/news/20010816/on-ace-inhibitor-you-dont-have-to-cough-up-lung What does your doctor say about the cough? Is your bp controlled?