Taking the meds described could a dry unproductive and aggravating cough, along with achy muscles and tiredness?

I think you might: Be talking about Lisinopril or an ACE inhibitor and maybe a statin drug for lowering cholesterol. These drugs also are used to lower risk of heart attack, stroke, cardiovascular disease in general and to reduce risk of kidney disease. I suggest taking the medications as they were prescribed. Side effects are possible, but not everyone has them. Your doctor decided the benefit outweighed the risk.