Bubbletrouble has spoken well with some good advice that I would echo here.
Your physician is of course the expert on medical things. The following is just my observations on life and not medical advice, or even knowledgeable discussion, and may not be relevant to your situation. Number one killer of SCUBA divers - Heart Attack. High Blood pressure increases the risk of coronary artery disease and with that comes an increased risk of heart attack and blood clots.
Medication may be effective at controlling high blood pressure and is a good tool in the doctors arsenal for managing it, but does not address the cause, just the symptom. There are many causes of high blood pressure including genetics, age, stress, lack of exercise, weight, diet etc. Most commonly in the USA high blood pressure comes from poor diet, too much salt, poor exercise habits and the resulting weight gain. Improving on the exercise front and the stress front by SCUBA diving more and doing other aerobic exercise (with doctors agreement) between dives (swimming, bicycling, running) and on the diet front by just eating healthier will normally lower the weight and with it the blood pressure. I know of several SCUBA divers who use to take blood pressure medicine before they started SCUBA diving weekly (or more often). Not saying that would work for you, just saying if your doctor clears you for aerobic exercise you may eventually reduce or eliminate your needs for the meds. I will also point out that you can be stick thin, exercise like a demon and still have high blood pressure and/or cholesterol due to other factors (stress, genetics etc). As always follow your doctors advice, but SCUBA diving can be an active part of your aerobic exercise program and blood pressure management regimen.
Example: Age 56, Height 6Ft., weight 145, BP 101/60 (it has gone up with age, I was 98/58). Ran marathons when I was 28 and yes I have genetics on my side). Dive most weeks, conditions permitting, often twice a week. Don't diet, just eat healthy, limit the junk food to once in a while and don't eat out too often. When I eat out I request they put half my meal in a to-go container
before they serve me. Most restaurants give you way too much food (and we patronize restaurants that give you larger servings over those that give you smaller ones) and we tend to eat it because we were told to clean our plates. Side note, Burger King's Whopper Jr, the size hamburgers use to be in 1960, taste good and only cost $1.00 and it is all you need for lunch once you start eating right sized meals and adjust to it. I add a Value Meal (aka Kids) milk shake for $1.25 and have lunch for under $3.00 that fills me up, has a treat (milk shake) and is not too expensive either in the wallet or calories/fats
(630 Total Calories Vs Whopper & Medium Shake 1190 Calories) department.
over 17yrs and no rejection. The only way it hampers my diving is I cannot lift/carry the BCD/tanks/weights out of the water due to a hernia. We have that worked out as I get my mask and fins on and get in the water, my husband passes the gear to me and I put it on in the water. If we have alot of chop, I put the gear on on the boat and he supports the tank for me as I walk to the edge and do my stepoff.
