A.V.
I had my fingers smashed in the car door as a child and didn't break anything. It just hurt - a lot.
He may lose the nail. I lost a toenail from dropping a soda can on it as a kid. They grow back.
If he can bend it, it's probably not broken. If you are still concerned, you can always take him in or make an apt. for the pediatrician. If you have an "advice line" for your insurance (like Kaiser does), you can call the nurse for guidance.
Hope he's feeling better by now. (not sure why the date on my post says Monday. It's only 9PM on Sunday)