Blood pressure medicines can have side effects. There is a class of blood pressure medications that can frequently cause a cough. This class is called the ACE inhibitors. Some examples of ACE inhibitors include lisinopril, captopril, and ramipril. The cough is generally a dry one but can be quite annoying. When someone gets this cough, it is usually grounds for the medicine to be discontinued. A different medicine called an angiotensin receptor blocker (ARB) can replaced the ACE inhibitor and control your blood pressure without the side effect of the cough.
Of course there are other causes of cough and allergies can be a significant contributor. If your cough only comes on when during certain seasons, or only when you are exposed to certain animals, then the allergies may be playing more of a role. This is an important thing to distinguish because an allergy cough can be treated with nasal sprays and pills.
I suggest that you schedule an appointment with your primary care physician
. He or she can examine you and determine the cause of your cough. If it is found to be caused by your blood pressure medication then you will probably be changed to another one. If it is caused by your allergies, then you should be tried on a new medication.