I've had three lots of root canal work done on three seperate occasions. All were done with the std type injections, before and also during the procedure. No problem with driving after them. Two out of the three were successful, the third went to abcess and I had that one extracted eventually
Won't pretend that it's a pleasant experience because it's not, but much better than having a tooth extracted, and having to live with a gap and subsequent tooth movement over the following years due to the space left.
Have the root canal work!