I'm happy that you have asked me to assist you with your child and hope that you can benefit from my many years of helping parents like you.
This is actually not really a pure medical term but rather just a "slang" term for lots of infection related white blood cells, called bands, that are present in the blood count. Unfortunately, lots of doctors use the CBC as some type of gauge of how sick someone is but it is really not very specific for what type of infection and a poor measure of the seriousness of an illness.
Having done this for over 30 years I can tell you that it is still frustrating to me to see doctors use the CBC (complete blood count) as a factor in deciding whether a child is sick enough to need an antibiotic as well as doctors throwing about terms that are confusing to parents and patients. There is no substitute for a good history, physical exam and perhaps a chest xray to determine whether pneumonia is present, and even the chest xray is not really necessary, according to the recent guidelines published by the American Academy of Pediatrics.
If your child has a respiratory infection with fever and evidence of pneumonia or bronchitis on physical exam, then antibiotics might be required, but I assure you that the blood count is not something that points one way or another toward making what is really a clinical decision by the doctor based on a good exam.
Don't worry about the "bandemia" as you'd be hard-pressed to find any scientific evidence in children that it means anything more than what a good clinician already suspects: that your child has an infection and needs an antibiotic. Albuterol is helpful to clear the wheezing in some cases and azithromycin works well for mycoplasma infection, though not particularly well for pneumonia. I suspect she has mycoplasma and will improve with these two medications, regardless of the blood count findings.
I hope this alleviates some of your concern about this but let me know if you have questions.
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