It must be really worrying for you, I dread the thought of my son hurting himself.
The fracture that goes straight across the bone isn't a problem as long as it's kept still so the bone can heal. The chip may need something doing to it though depending on how bad it is.
In the mean time, try to keep her arm elevated if you can, this will help to reduce any swelling. Ibuprofen for pain relief and inflammation, make sure she moves her fingers as much as she can to help the blood flow. Keep an eye on her fingers, if they don't pink up after you squeeze them pretty much right away or go blue/purple then take her straight back to A&E.
Did they x-ray her elbow aswell?