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The drug Lisinopril, an ACE inhibitor, is notorious for producing a cough with its use. This is due to the a hormone known as Bradykinin which is released excessively with the use of this drug, Bradykinin puts the airways in spasm and this can produce a cough with a wheeze and sometimes a reactionary secretions as well.
I would suggest that you discuss this with your physician, so that s/he substitutes this drug for an Angiotensin Receptor Blocker (ARB), which has the same effects for lowering blood pressure as the ACE inhibitor and very little side effects. These drugs are Losartan, Valesartan etc. They are now largely replacing drugs like Lisinopril and Captopril due to the side effects of the later two.