buy yourself a new blood pressure monitor, take your blood pressure a couple of times a day for 2 weeks and make a note of the time and measurement, make an appointment to see your doctor and take the monitor and your results with you. the doctor can then check the monitor against his own results to make sure it's accurate.
i believe they need to monitor your blood pressure a few times before they put you on tablets. i would go along with what your doctor recommends. it is far better to take blood pressure medication if you need to, than do without and risk the consequences.
i too suffer from 'white coat syndrome', and take blood pressure medication. my home monitor has reassured me. my doctor still takes my blood pressure when i go and see her, but takes more notice of my own results.