It would be helpful to know what the exact numbers were when your BP was high. However, propranolol is a good medication for both high blood pressure and a rapid pulse. It's in the category of drugs called beta blockers, which are used both to lower BP and to regulate the pulse.
EVERY medication on the market (and many herbal preparations) have side effects. If you read the data on aspirin, acetominophin, cold medications, etc., you would find a long list of "possible" side effects. On the other hand, high blood pressure itself can cause major problems if not controlled...it can lead to heart attacks, strokes, kidney damage, and more. So, whenever your doctor prescribes a medication, you need to weigh the risks against the benefits.
I did take propranolol for many years. In fact, due to the type of high blood pressure I have, I was on 360 mg a day. I had no side effects whatsoever.
My suggestion would be for you to get a home blood pressure monitor and keep track for a while. If you're consistently getting a systolic (top number) of over 130, or a diastolic (bottom number) of 90 or more, or a combination of both, then it's important to get your BP regulated.
Ruth