wmdeal, I had the same issue you did. Here's what happened with me:

I did fine at MEPS except for the blood pressure.  They took 3 machine readings and averaged them, and the average was a bit higher than the limit.  Therefore, when I saw the doctor, she checked it manually...still a bit elevated.  I guess at that point I was temporarily DQ'd, but they let me go to a private doctor on my own and get three readings, 15 mins apart for two consecutive days.  When I did that, I got readings all below the limit, then submitted the paperwork back to MEPS and they qualified me with no issues.

Like you, I have normal readings until I'm put on the spot. Just remember all those healthy blood pressure readings you always get and you won't have anything to worry about.

Do not trust the ones at a pharmacy...please. I would recommend that you visit your local fire station and request a blood pressure reading, take a note pad to write down the day, pressure and pulse rate, let them know your anxiety issues and that you are monitoring your blood pressure for several days/weeks for your doctor. They should be more the happy to do this for you, we do it all the time in my department. Go everyday you can if not s couple times a day, this will get you more comfortable with it. Another thing that will help blood pressure issues is reduce salt intake and eliminate caffeine intake completly...take several deep breaths and relax while the get the blood pressure cuff and place it on your arm.