If you have some Witch Hazel you should soak it up in some small towels and wrap his hands in it for at least an hour. It will help with the swelling. Repeat offen if needed. Also taking some aspirin will help with swelling or Aleve.
The benefits from icing an injury tend to diminish after 48 hours so there is still plenty of time to do so. Ice the affected area for 15 minutes, rest for 45–60 minutes and repeat as necessary. Moving the ice around and elevating the affected area helps to reduce the swelling. Good luck.
Might immobolizing the fingers help? He might be constantly reinjuring the area. I don’t know which fingers are bothering him. If it is some sort of sprain I think it will help.