I'm sure your doctor took into account 'white coat syndrome.' This is where you have a high bp reading in the doctors office due to nerves. Or maybe you took an ibuprofen which can push your bp up, etc. You should not have to manipulate things to lower your bp. When I checked bp at home, I was told to do it first thing in the morning in a resting position.
It sounds like your BP is one that will respond to certain things so make some significant life style changes without all of this number to number analysis. Work out 5 times a week at a moderate, brisk to vigorous pace. 30 minutes is the recommendation and you CAN break it up if need be into 10 minute increments. But do it religiously. Also, you sound over weight. What is your BMI.? Eat a healthier diet lower on fatty foods, processed foods, less sugar, more vegetables and fruits. The DASH diet is one that is touted as vey successful. It's not a fad diet but more a way of eating for healthy blood pressure. Quit smoking if you smoke. (you don't mention).
A doctor's office will always be more accurate than an at home cuff. They've identified you as having hyper tension from ONE reading? I do doubt that. But they would probably like to you to follow up. Don't mess around with it. If you are going to take the approach to see what you can do on your own, give yourself 3 months to lose weight and work out 5 x a day. I would not try to argue this or that based on you lowered it after exercise or your arm is too muscular, etc. The doctors are not trying to hurt you--- they want to help. If you doubt, get a second opinion. good luck