I understand your apprehension but without veterinary treatment your chin very well could die. If he is still limp, he is still in shock, and the longer they are in shock, the less of a chance they have of pulling through.
He needs to be treated, because they usually are not able to pull through on their own once they get passed a certain point.
It is imperative you get him to a vet. Start calling vets in your area to see if there are others that would treat a chinchilla. The longer you wait, the less his chances are.