What is the relationship with high neutrophil and asthma? I have had morning cough from nov-jan. Chest X-ray is clear; wheezing and sob on exam.

Not too much. A high neutrophil count on a CBC (complete blood count) can be found after a patient has taken Prednisone (oral steroids). It can also be seen under times of "stress" including bacterial infections. There are various forms of asthma where there is high neutrophil count in the sputum coughed from the lungs-this includes some occupational asthma and severe non-allergic asthma.
Asthma and Cough. Asthma can be exacrebated by sinusitis, allergy, reflux disorder, or infections (viral, bacterial or fungal). Neutrophils can be related to many conditions. See a pulmonologist, allergist, ent, etc. For more answers. All too often asthma is only treated as a wheezing disorder when ther are many underlying issues that can be managed and often eliiminate the asthma.