Can blood pressure medication or cholesterol medication cause your hemoglobin a1c to be elevated?

Yes, there is a low risk of glucose intolerance which can occur with the use of statins (the primary drug class to reduce cholesterol). This can lead to elevated Hba1c, which is why it is important to eat healthy and maintain normal BMI even when one is taking statins. Certain beta-blocker and diuretics can increase Hba1c in diabetics, but I'm not aware whether this occurs in non-diabetics.