Do we have a case for Misdiagnosis/Malpractice?

My 11 year old daughter fell down a flight of stairs at a college basketball game. (Just an accident) We immediately took her to the ER. Her right cheek and eye, left forearm, and left foot were all swollen and bruised. They x-rayed her arm and foot. The ER doctor said she didn't see any breaks, but she would have the radiologist look them over and call if he found anything. She told my daughter that it would be extremely painful because the bruises and swelling were severe on hard to break bones. She gave her no limitations. We were in and out in about 25 minutes. For the next week and a half my daughter attempted to participate in volleyball conditioning, crying to her coach and my husband and I. She woke up everynight in pain. Being that she has never endured 'pain', we just kept encouraging her to work it out. Finally, I called our doctor and he had her arm x-rayed. She had 2 breaks in her wrist and one in her elbow. I immediately called the ER and requested her x-ray films and reports. The next day the ER doctor called my husband and apologized that she didn't see the 2 breaks, but the radiologist confirmed that she had them, they just didn't let us know. The thing is the first x-ray showed 2 breaks, now there are 3 breaks. We then had to see an orthopedic specialist who put her in a cast. Then later had to see a pediatric orthopedic specialist. While her wrist is now healed, her elbow is still giving her problems. She still can't extend her arm all the way. On top of all of this we have bill after bill for all the doctors, hospital and radiology. Although our insurance is decent, had this been caught at the ER, we would have been covered 100% as an emergency. Plus, my daughter wouldn't have been going through volleyball conditioning and enduring all the pain prior to the correct treatment.