These headaches are extremely unlikely to be related to the nasty fall in anyway that can be identified and treated.
Did your GP assess her neurology, ie do her reflexes etc, and look in her eyes?
When are the headaches worst? Is it when she is at school or in the morning or evening?
Can you identify anything that brings on the headaches each time they occur?
Does anything make them worse when she gets them or does anything make them better?
Does she feel sick/been vomiting?
Does she complain of any disturbance to her vision during the headache?
Does she suffer from travel sickness?
Any family history of migraine?
You will not get an x-ray, or at least you really shouldn't, as they will tell you nothing about what is going on/cause of the headaches. If the doc, either gp or in A+E, feels that your daughter needs imaging then you would be looking at a CT scan as a first line and this comes with a significant dose of radiation so this risk needs to be balanced with any possible benefits.
To go down a non-physical route, and not wanting to offend you, does your daughter gain anything by having these headaches? I'm not trying to suggest that she is malingering, but that perhaps there is something that happens when she gets a headache that somehow makes it seem like a positive thing. It may not immediately be obvious to you what the "benefit" is.
I find it interesting that the school have not contacted you with concerns yet she is visiting the medical room so frequently and also that her headaches seem to have devoloped quite quickly after her neck pain resolved.