I had that done when I was a kid. Didn't hurt one bit and it was over in 90 minutes. They use little hair fine needles to administer the Novocaine and after that you feel a little pressure as they do their thing.
All they do is cut the nail down both sides and remove the edges. In my case they trimmed off a little of the flesh on both sides to make a better shape. They did the right first week and the left the next week.
If you imagen a curved shield with a round top that is smaller than the rest, you get an idea of what your toenail looks like if you cut it round or too short. Those top corners are what's digging in and giving you grief.
Go to a foot specialist and have it done. After it heals up in a week or so you'll be damn glad you did. Trust me, I've had happy feet for over 40 years now.
It does require a little maintenance and they'll show you what all to do.