Hang On!
Check with the hospital! How old is your dd?
She shouldn't be NEEDING painkillers that frequently for very long, no more than a few days at the most.Every 4 hours is a maximum dose, not compulsory, and you MUST make sure you don't go over the daily maximum. If your dd is sleeping comfortably at night, please don't waker her every 4 hours for more painkiller!
Did the wrist require manipulation under anaesthetic, or an operation, or was your daughter just seen and treated in A+E?
The doctors receptionist is WRONG, you can get it on prescription for a child, but you shouldn't need more than a bottle, so it wouldn't cost a fortune.
You don't have to buy branded Calpol, either, if you ask a pharmacist for paracetamol, and give the age of the child, they can dispense a much cheaper variety.