Ed is correct from the perspective he described, however, there is another prespective
and that is your pulse rate decreased with higher blood pressure and/or changed very little.!? Usually the heart rate increases when blood pressure increased unless one is on medication. You don't show the dynamic relationship that is expected without medication!
For some insight, by exercising the heart speeds up so the blood can reach your muscles. It may be possible for your heart rate to double safely, while your blood pressure may respond by only increasing a modest amount (there is a compensation aspect). It seems the heart rate and blood pressure tend to both increase during exercise, and decrease during sleep.
I am a bit confused about your Doctor because even the blood pressure in your left arm seems too high (Diastolic). At first glance I would think maybe due to your age, your arteries are stiffening a bit and medication is required to lower your blood pressure. However, your right arm shows a high difference. The American Heart Association believes a difference of 10 or less to be normal and anything higher warrants investigation. Yours is much more than 10 and could be a sign of something like heart disease. Do you have any kind of symptoms related to your heart, such as shortness of breath, chest discomfort, fatigue?
I would go back to your Doctor and explain the recommendations of the AHA, and if he/she doesn't feel there is a problem I would tell them you are going to write to a Cardiologist for an opinion on this, and actually do that. My guess is, they may decide to refer you in case they are wrong in their decision.
I can't understand for the life of me why they won't send you to a Cardiologist to be on the safe side, what harm is there. Have they at least done a EKG on you?