how can we diagnose pertussis in newborn ? differential diagnosis ?what is treatment ?  how can we manage  cough until cyanosis ?

I would recommend reading this page from CDC. Azithromycin seems the drug of choice.
https://www.cdc.gov/pertussis/clinical/treatment.html

This paper on nosocomial spread of pertussis is another good read: https://www.sciencedirect.com/science/article/abs/pii/S0195670113003253

 

thank you