Is the cough associated with bp medicine something that gets better in time or should i request a new med?

If ACE-Inhibitor, no: Unfortunatley, the cough with ace-i is idiosyncratic (just happens / no good predictor), and rarely improves over time, so likely should ask for medication change. Sometimes other ace-i will not do it, so trial of another in same class not unheard of, or dr could switch classes for you.

ACE cough: If you are on an ace inhibitor (angiotensin converting enzyme inhibitor) medication and have a persistent dry cough, it might be attributable to the medication. If so, the cough can be alleviated, while still treating ones blood pressure, by switching to an arb (angiotensin receptor blocker) medication.