OK, you KNOW your DD and how likely she is to have reacted to something, and how much she sounded like she was in pain/distress or just upset and sore.
In general, if I think a broken bone in the legs/foot, I think straight to A&E and it depends on the severity of the apparent injury, the patient's ability to move themselves or not, and options available at the time (other transport immediately there, people who can assist moving into that transport, how bad is traffic at that time of day for a car v taxi v ambulance etc) on whether I'd insist on an ambulance being called.
In general, with broken bones further up (arm, shoulder, ribs etc), I would assess the person on severity of injury/pain etc but be more likely, while still saying A&E, to suggest getting there by other means than an ambo.
Anything to do with the head, unless ambo would take longer, I'd be inclined to call ambo for A&E.
Also, anything where blood is either flowing very freely or spurting, or where patient is showing signs of shock, I'd tend to call ambo at least because of assistance of paramedics, lots of bandages, monitoring equipment and drugs.
I am a trained occupational first responder (beyond first aider level) and involved with various sports and outdoor activities, so have had to deal with a few different things in my time. None dreadfully serious - but I know my limits too.