How can normal blood pressure suddenly rise and stay on the high side

I am a 75-year-old female. I left an extremely stressful job in March. My nerves and my BP were frayed and high. However, my BP is fluctuating and staying on the higher side.
The BP ranges from 127/71 to 133/75. My doctor gave me a BP medication, but it caused side effects.
My doctor is driving me a little crazy and insists I have an at-home BP machine. The at-home BP machine instructions read: Don't eat or drink anything, and still completely still, feet flat on the floor, for at least 30 minutes before taking a reading." Sitting completely still is difficult.
The readings today started at 158/70 and ended at 133/75. Three or more readings are required. Two days ago, the reading started at 137/66 and ended at 127/70.
What is a serious BP? I'm really concerned and fear going back to the doctor.