Gram stain and culture results for sputum are confusing!!

So my daughter's doctor asked us to test her sputum to see if she has an infection because she's been coughing for too long now (about 2 months). She's 4 and a half years old and this is the first time we have to face this so we're still not familiar with it. I got her results on the phone and was told that the gram stain showed no WBC's or neutrophils, but the culture stated that she has Haemophilus Influenzae which was also tested for sensitivity and resistance. I guess my questions are: Does the fact that there are no WBC's or neutrophils rule out the possibility that she has an infection? If that's true then how did she culture H. Influenzae? OR Does it mean that the bacteria is there but there is no active infection? And if that's the case do these types of "non-active" infections usually require antibiotic treatment? Sorry if I sound like I'm rambling out my questions but we're really confused and her doctor is going to be out of the country for a week and we're not sure what to think until we get some answers. Thank you all in advance.
Source: Cystic Fibrosis Families Forum - Category: Respiratory Medicine Authors: Tags: Families Source Type: forums