I too am very jittery when they need to bring out the drill. They used to give me nitrous....I even had my own personal rubber/plastic nose thingie that I would bring in. I would also bring a walkman (lol! yes, i'm old). It helped immensely. My favorite CD for the dentist chair in those days was Paul Simon's Graceland. It took me far far away and I didn't have to care about the drilling sound.
Once I forgot the CD so I put on the radio...Howard Stern...that didn't work because I would start to laugh.
Anyway, problem was nitrous kinda makes you feel queezy afterwards and I got tired of that feeling. Now I just grip the handles of the chair with all my might.
Hope you recover ;-)