J.D.
Hi A.-
Usually these kinds of floor burns or scrapes, as WebMd calls them, heal on their own, but sometimes complications arise. I've had a couple of these on my knees in my life. One summer while wearing shorts, I fell on a sidewalk and scraped my knee. It didn't seem like a big deal at first, although it really hurt. I cleaned it with peroxide and then continued to clean it with peroxide, which is wrong. It didn't heal and I finally went into the doctor who said I was on the verge of blood poisoning. So, my lesson there was to clean once, then let it heal. The peroxide was killing off the good bacteria that was trying to heal the wound.
That said, I don't know if there is really anything that you should put on it. It needs to develop a scab to heal and putting ointments, etc. on it might prevent that, as I did. Read the WebMd page I found for you and make sure it's not infected and/or check with your doctor.
http://www.webmd.com/a-to-z-guides/scrapes-topic-overview
Keep an eye on it and if you see a red streak running from it, get to the hospital immediately, as that's a sign of blood poisoning. I'm sure that won't happen, but just be aware.
As for the pain, I think you should have the doctor give your son a note so that he is able to wear shorts to school, assuming he won't be walking in cold weather! I don't know if it's good to wrap anything around it, either. The air helps dry it and makes the scab, I think. I would call the doctor first. The school can't argue with him/her. Good luck.
J.