You could have a hairline fracture of one of the sesamoid bones. These are used heavily in the toe-off phase of the gait cycle. You will need to get it evaluated by a foot specialist to confirm as there are other things that could cause similar symptoms including strains to the tendons attached to the same bone.
Such fractures can present as pain that comes and goes, often made worse by faster running which causes increased toe-off pressure and could also cause a feeling of numbness or weakness under load.
You won't necessarily have pain before or after a run.
In the short term, taping may help to give support and reduce pain.
You don't need to rush off to the GP unless the standard conservative measures don't help.
regular icing (2-3 times daily) to bring down the inflammation for the first few days
regular daily warming followed by gentle calf stretching
gentle massage of the tendon itself
If she runs regular, it might be wise to get her into a basic daily stretching routine (ideally after each run) though kids are generally a lot more flexible than adults.
If symptoms don't improve in a week or two with these measures then see your GP for a referral to a physio who might recommend slightly more radical therapy (like gait correction) though I doubt it would come to that.
PF can take months to heal properly even with the appropriate and well established treatment protocols, depending on how badly damaged the facia is and whether it's caused any collateral damage such as a heel spur - so you should get a scan done or at the very least an x-ray.
You need to get your gait analysed because excessive pronation can be a strong contributory cause of PF and this will lead to recurrence or chronic issues if not dealt with. Any anti-pronation measures (such as say an orthotic) will need to be in place even when walking, certainly during the early stages of recovery.
I presume you aren't overweight, but if you are, it will help to lose some as this can also predispose to the condition.
As others have mentioned, regular stretching of the plantar flexor muscles, in particular the calf (gastrocnemius and soleus) will also help as a longer term preventive measure.
Other than that, you are going to need a lot of patience as PF is one of the more frustrating injuries to shake off.
You are clearly new to running so you can be forgiven for thinking that painkillers might be the answer to your problems - but they are just about the worst thing you can use in terms of trying to combat an injury.
Taken on a regular basis, all they will do (if they work at all) is to mask your pain - your injury meanwhile will continue to get worse.
Take it from someone who's been in the running game for over 40 years and still going strong - pain is your friend, not your enemy.
It's your body's way of alerting you to the fact that something is wrong and needs dealing with and the quicker you deal with it the better.
The following three things are usually the most important.
You need to know what's wrong
You need to know how to put it right
You need to know what caused it so you can avoid a recurrence
Running injuries can occasionally be vexing to deal with, but most are well documented, with well established treatment and prevention plans, so once you know what's wrong the other two often follow quite easily.
However, many injuries occur simply from overuse, especially with new runners, and don't necessarily have any one specific cause and there are a whole bunch of first-line-of-attack measures you can try even without pinpointing exactly what's wrong. Many of these are used in treating most injuries anyway.
icing the injured area (where the pain is)
deeply massaging the affected part(s) - after warming them up
gently stretching the muscles/tendons affected by the pain
strengthening the affected muscles or their antagonists (muscle balancing)
Often with new runners, there is a tendency to do too much too soon - your body needs time to adapt and pain is often an indication that you have pushed a bit too hard. There's even a 70% chance you have pronation problems and you might not be running in the correct shoe for your foot type.
However, before getting bogged down with too much running science, just try the conservative measures I mentioned above and see how your injury responds. Don't start running again until you are free of pain and even then start gently and build up slowly. If your symptoms recur in spite of your efforts then get back to the forum or see a physio.
I would always recommend the following to new runners
get a book on basic running that is aimed at beginners
get a book on stretching for runners
get a book on self-massage techniques
These books will not cost the earth, will get you up to speed with the basic know-how's of running as well as the pitfalls, will keep your body in a good state of maintenance and even if you do get injured again (and you probably will) could save you countless hours of injury recovery time.
Running well and largely injury free is not a given. You have to do things other than just running to minimize the impact of the great stresses that the activity places on the muscles and skeleton.