Don't let that arm rest too long, I cut a finger (14-15 stitches) about 55+ years ago, it took almost a year of ball squeezing to get normal movement back after being in a metal splint for a month.
My worst bike accident was when I was about 13 (early 1950's Cleveland Ohio) I went over the handle bars at 20+ miles an hour after hitting a hole in the road. Lucky me the road was just tared and gravel, did a belly flop, clothes cut to ribbons, skin lost from all frontal areas, except face, the neighbors called the cops, when they came they loaded me and the bike into the back of the cop station wagon and took me home. My mother took one look at me and said take him to the hospital!, and they did.
At the hospital, they cut the remainder of my clothes off down to my shorts, cleaned me up, bandaged me by rapping gauze around arms, legs, etc. (looked like a mummy) gave me bus fare to get home. The real pain was when my mother had to change the bandages my tissue had adhered to it. I still have black dots on my forearms where I guess the did not get all the stones out.
I was thinking now days there would have been the cops, fire department, parametric, ambulance, etc, and a lot of $ changing hands, back then I do not remember that they even asked were I lived, they just took care of me and sent me on my way.