I have to agree with the expert above, high neutrophils (and therefore high total white cell count) is classic presentation of a bacterial infection. The timing of the blood test in relation to her symptoms is very important. So it is worth retesting her blood if this has not been checked since the initial pneumonia. I would also suggest urinalysis, and if the fever returns then blood cultures to check for presence of bacteria in the blood.
Children often develop fever which is non-specific and a thorough examination to include throat, ears and urine is standard. It is very important to check that she has no lower back or flank pain as a kidney infection would cause the symptoms that you mention.
What antibiotic was she given for her pneumonia? Did they ever tell you what organism caused the pneumonia?
Thanks for the extra information, the ingredient is ceftriaxone which is a pretty powerful antibiotic so would have tackled most infections althugh sometimes the course is extended to 14 days.
When was her last blood test taken?
This peak in blood levels seems to correspond to the high fever that she had on completion of the course. That would match an infection, but is non-specifc to type or location of infection.
As this has been a week, then repeating the levels and a clinical examination to include temperature, heart rate and urinalysis would be in order.
You mentioned that she 'could hardly walk', was this due to pain?
How is she now?
I am glad that she is seeing her doctor, it may be that she is on the mend however do make sure that she gets a top-to-toe examination tomorrow to make sure that ears, throat, lungs and kidneys are all checked out.
And blood tests should include full blood count, white cell count and electrolytes/urea as well as urinalysis dipstick.