Thank you for your query.
This is a common problem with defects like this.This is actually due the pain in the nerve
endings which were meant to supply at the nail beds.This will be a recurring from from now on.Oral painkillers and local counterirritants can help.The best person to help you out would be a plastic surgeon who specializes with fingers and hands.
As for the nail..if its getting embedded in the soft tissue
it has to be dealt with.
Hope this answers your query.Wishing your child a speedy recovery.Have a nice day.