I think your BP is probably fine. Your doctor mentioned White Coat Syndrome and it seems that may be your issue. I don't think there's anything wrong with your monitor. You checked it at the Dr's office. It's just that you are more anxious at the doctor's office than you are at home. I'm the same way so I don't worry about the readings at the doctor's office. It seems you have a very good doctor that realizes this could be the issue and isn't in a hurry to put you on meds if you don't really need them.
Eat healthy, exercise and cut down the stress