I wasn't properly anesthetized for my repair and it was awful. The doctor doing the repair didn't believe that I could feel pain, but I could. I had a number of stitches - about 10-15 or so (don't know for sure as I didn't ask). The indignity of yelping and kicking my legs (and being subjected to unnecessary pain after complaining) after the birth like that still really upsets me.
It was not just pressure or the feeling of the thread going through. I could feel everything for more than half of the stitches. It was pretty awful.
Talk to your HCP ahead of time about making sure the local has taken effect and listening to you. I know my midwife would have listened. My doctor told me it was "just pressure." Like I can't tell the difference.
Healing wasn't bad. The stitches were uncomfortable until they fell out, about 10-15 days after giving birth. It was just a little tender and awkward until then, and after then felt like new.
ETA: If I had still be holding my baby when getting stitched up, I doubt it would have been as much of an issue for me, because she would have been a fantastic distraction. As it was, they had taken my baby to the other side of the room for weighing, evaluation, etc.