Hi, I think right away we can dispense with Chronic Neutrophilic Leukemia since "CNL is an extremely rare disease. To date, the World Health Organization (WHO) has only reported approximately 200 patients who have been diagnosed with CNL."
I believe the WBC goes much, much higher in the common non-neutrophilic myeloid leukemias, btw.
So can WBC go as high as 21 from prednisone? Yes, but that degree of rise is more than average.
My father who had lymphoma and was sometimes put on prednisone got to around 20.
Here https://www.ebmconsult.com/articles/glucocorticoid-wbc-increase-steroids we have a review saying that there is a lot of *variability*, and "Some studies have shown increases in WBC counts greater than 20,000/mm3 ..."
Here's a study about variability "Prednisolone Pharmacokinetics and Pharmacodynamics in Relation to Sex and Race" which also talks about estrogen levels: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4207281/
10mg of prednisone isn't that large a dose; e.g., for immune suppression 60-80mg us used. Here, dosage is talked about https://www.ncbi.nlm.nih.gov/pubmed/7304648 and also mentioned is that lymphocytes can be reduced (lymphopenia), which you also have.
So your level of neutrophila is possible from the steroid, though not average. Maybe you are just very reactive. But some of that might also be a reaction to infection. During infection, new neutrophils are rushed into production, and those new troops can be detected in a blood test as "bands" because they look different than the mature neutrophils ("segs"). Were those figures on your tests?