Although blood pressure medicines like ACE inhibitors can cause persistent dry cough but these symptoms can be due to congestive heart failure ( cardiac asthma
You must consult a cardiologist
and get relevant investigations like ECHOCARDIOGRAM
done to look for any cardiac involvement.
The chances of cardiac involvement are much more in a longstanding diabetic.
The other possibility is asthmatic bronchitis.
In case you get a clean chit from cardiologist,then you may consult a pulmonologist
for necessary investigations.
Treatment would depend upon finding the cause.
There is no point giving anti biotics or steroids without any rationale.