It is difficult to sew up lacerations on small children. Oh, in the bad old days we would just hold them down, but that is really not a very kind thing to do. Besides, it tends to sour them on the medical system generally and if you give a kid a horrible experience you are just making life so much harder for the next doctor who has to treat him.
You can medicate kids. We have some short acting stuff that makes them pretty silly and happy, and gives a temporary amnesia for any discomfort they may experience. But so called "concious sedation" involves a lot of paper work and a small element of risk. I do it when necessary but only then.
Most of the time you can get by with showmanship.
There is a topical anesthetic gel that works pretty well on the thin skin of kids; if you can get it on there and keep it held in place for a half hour or more. I like this stuff a lot. Sometimes you can get a parent to put on a glove and hold it in place. Other times, like a two year old I had recently, the injury is a place like the forehead where you can hold the cotton ball in place with an elastic "Ninja Turtle head band". I have actually learned the names and distinctive color schemes of all four Turtles.
Then it is simply a matter of getting the first stitch in successfully. Kids are smart and realize that if the first one did not hurt the rest will also be ok.
Lately I have started telling the kids that my Secret Identity is: Spider Man.
One of my ID badges had a photo that faded prematurely so I put a Spider Man sticker over it and just kept it when I got my new one. It makes a sort of Kid Logic....he has a Secret Identity badge and he has Spider Man web material that he is going to use to fix the owie. You just need them intrigued by the possibility for long enough to get the job done.
Ah, but we live in suspicious times, we do. So to persuade the young doubters I sometimes have to take the special marker we use for drawing on skin and do this: