My daughter has really bad back pains and she has a hard time laying down flat what medicene should she take?

Over the counter: I would initially use over the counter tylenol (acetaminophen) or Ibuprofen and if the discomfort persist she should be seen be a physician.

See a doctor: Back pain can be caused by a variety of reasons, some minor, some serious. If she is having a hard time laying flat, i would suggest that she see her doctor rather than just take medications. Unless you know the cause, it is impossible to know the correct treatment.