Dentistry is strange anyway. Last night, I had a filling done. I'd had an injection & anaesthetic cream on my gum which led to most of the tooth being numb but there was still a raw spot. The dentist couldn't explain why this was the case, he said that some pain is psychological, not overly surprising but not really the answer if everywhere else on the tooth was ok & it was just a certain spot that was agonising. I ended up having another injection & the anaesthetic then had the right effect. So 2 injections & some anaesthetic gel.
Anyway, my point is that we're all different. We all have different pain thresholds & just go with what you feel is comfortable. I apologised to my dentist for being a wimp but he was good to say that I wasn't lol, I felt like it being given the second injection. But, if you have a good dentist, they'll be understanding, will make sure that you are comfortable & then the whole procedure should be straightforward. Plus, there will be less pain afterwards due to removing what's causing the problem. Oh & my wisdom teeth never came through, which is a good thing..I think. But I have had a different tooth extracted before, as it had grown out at the wrong angle. The tooth was at the top & the back & other than breaking a bit in the process, the procedure itself was relatively simple.
Good luck for you with your work. I'd advise going private with your dentist. I have a private dentist and I'm happy to pay more. But, it's up to you as to whether you can afford more & if you would like to use the money by going to the dentist. As has been said above, the NHS dentists can be very good too.