You might be surprised. "White coat hypertension" is well-known. Someone with a reliable set of readings from home would be more convincing than someone who says "I get it read at Walmart/CVS once a month and it's ok".

Your doctor's office's monitor isn't incredibly accurate. If you want accurate, you need a mercury sphygmomanometer to measure the pressure. Unless fundamental properties of the universe have changed, it will also be comparable to any other readings taken with mercury.