Need opinion...would you go on this medication?

So for many years I've had white coat syndrome, where because you fear your blood pressure might be high you get SO nervous, that it goes really high while being checked. I can only get an accurate reading when my doctor does not tell me or announce she's going to check it. Then I really don't realize what she's doing till the end, because we are chatting a lot. It's normal at rest, without anxiety.

So she knows that I get anxious on other occasions outside of the office, in traffic, etc my blood pressure does probably go up during those times, a few times a week. But, it goes back down to normal in a couple minutes. She wants to put me on a blood pressure medicine, to be preventative, so that down the line, my heart is protected and that the vessels aren't harmed over time. But my pressure is normal. It's only a few times a week it goes up for a miniscule time. I've read that anxiety does NOT HARM THE BODY. My therapist even thought it's a bit much to go on a med if it's not ACTUALLY regularly high.
I'm afraid of it now going low if I went on it. Would you go on it? It's a low dose, but still 🤔🙁