When Strider gets cuts and tears I put a good diaper rash ointment on it.
One of the "natural" ones, like Burt's Bees, or California Baby ones. They are extremely soothing, have a variety of oils with antifungal/antibacterial properties, and are nice and greasy which helps seal dirt out of the wound and keeps the skin supple so that it doesn't crack open again as it heals. We've had better success with them over regular antibiotic ointments and for pain control.