It is called a papoose, it is like making the kid into a burrito. I believe they only use it for stitches and staples, but not the glue. My kids have had the papoose and it is necessary, esp for a facial injury. For the more extreme stitches one of my kids, he was wrapped in the papoose, the wound was cleaned (mainly flushing it out), the stitches were put in (10), a dressing put on, all done.
If the wound is to the face, you want the steady hands to minimize the scarring. A papoose helps that.