Honestly, I don’t know the answer to your question.  It probably depends on the child and the severity of the CAH.  I do know that when my daughter broke bones (there have been many instances - each arm at the wrist, ankle, toe, thumb, forearm)  she never had a shot.  She did take a stress dose of her oral medication and was just fine.  Even that did not happen immediately.  It was probably 30 minutes or more before she received the stress dose.  We stress dosed for 24-48 hrs depending on her pain level.  Now, these were simple, clean breaks or hairline fractures -just your everyday kinds of breaks that kids have when they fall down, etc.  I have always been told to give the oral medication unless the child is vomitting or diarrhea or very high fever or otherwise unable to take the medicine orally.  If it was more a life threatening injury, I would give the shot.