Arnica is an amazing homeopathic remedy that is exceptionally easy to use at home for acute, first aid conditions. I have used it repeatedly to address the frequent bumps and bruises that are an inevitable occurrence of being a child... or the parent of a child.
Arnica is indicated with almost any trauma injury that threatens to cause a bruise or swelling. The injured area is always worse with touch or pressure, and commonly presents with black and blue discoloration. It can also be used for muscle soreness from over exertion, for example lifting weights or shoveling snow, etc. Arnica works very well when used in conjunction with ice over the injury.
It is great for a bump on the head. The sooner you can get the Arnica in the child's mouth the better.
Arnica is available in most health food stores in a 6, 12, and 30 C (or X) potency. Any of those will do. I typically give 3 pellets every 15 minutes for 3 doses.