I am not an AME but I would be asking quite a lot of questions of a 36 year old with hypertension I am afraid. I suspect the AMEs will want full reports from your cardiologist. BUT this is rather a general observation and there are many reasons you may be OK so do discuss your concerns.
You also need to discuss prognosis with your cardiologist as you need to ensure you dont spend money and time to fly professionally only to have your career stopped prematurely. Sorry, but hypertension in young people is rather different from the usual high blood pressure in the older person. The latter is indeed common and 'normally' managed with a tablet or two and little further issue
As to taking the drug(s) you would not be able to fly for a period after starting or changing any drugs. You should take the drug(s) at the same time every day ideally in the morning. Changing the time of administration due to flying rostas seems to me to be a recipe for disaster. Side effects if any tend to be continuous and not just intermittent after each dose