possibly having baby @ 35w..

I really need some help / advice.

Family history : HIGH BP. Passed down on to me.. ofcourse. Have been on meds for over a year now and they are successful, except when I am at the dr office my pressure is always higher than normal, I have recordings of my readings at home and they are ALWAYS perfect and within normal ranges.

My l&d office just called me and told me they want to see me in a few days for an hour to monitor me and the baby to make sure everything is okay considering my high readings at the office , great pre cautionary step I ageee with that! However, if it’s high (99.9% chance it will be because white coat syndrome) , will they induce me at 34 weeks and 4 days if it stays high ? any success stories of babies born at 34 weeks or even before then ? any advice on what to do or what they are going to do when monitoring me ? I’m a first time mom and I’m freaking SCARED.. 😢