Remember those water filled plastic teething toys? My daughter is well passed teething, but I popped them into the freezer and now when she has a "hurt" I offer her a frozen frog or fish to put on it. Cold compresses are good for a lot of things, but playing with an ice cold toy is also a distraction from a bug bite or scrape.
Just be sure to keep away from the soft plastic liquid-filled teethers. They were part of a safety recall last year.