What should one do at the dentist with drilling - wear noise blocking headphones or not?
I've read many threads and the consensus seems to be to
not wear plugs at the dentist. Dental drilling generates physical vibrations inside your head and the earplug removes an outlet for these, leading to an increase in perceived and actual loudness. You can try this easily - go to dentist, plug ears, unplug ears, you'll see that being plugged is worse in this specific case.
The recommended practice is to reduce noise by asking the dentist to drill 5 seconds, then stop for 10. You might have to shop around for a sympathetic dentist. I was brushed off by 2 older docs, and the third one, a 30-something doc was the charm, he's superbly understanding. (Also superbly expensive haha.)
Finally, focus on developing excellent dental hygiene. Brush twice, use mouthwash twice, floss once every single day with quality brushes, paste, mouthwash and floss. The single best thing you can do for dentist noise is to prevent it by preventing cavities. I had to go to the dentist every year like clockwork; this year I picked up these habits and 0 new cavities, plus all gum inflammation is gone, no more bleeding when brushing etc, it's just great.
(One of my incisors is artificial and I broke a piece off by biting into something hard, that's why I need the aforementioned sympathetic doc - not a cavity.)