Brief Answer:
I would like to give some bronchodilator with azithromycin

Detailed Answer:
Hello

Thanks for the query

I can understand your concern.
After going through the details I have concluded that this can be due to

1)Persistence of cough after an acute episode of viral infection.
Most common cause of cough,cold with fever in this age is due to some viral infection.The infection may localize to upper respiratory tract(URI) or can extend to involve the lower respiratory tract(LRTI).
Even after subsidence of acute upper respiratory tract infection the cough may persists for 1-2 weeks in some cases.
The involvement of lower respiratory tract is a serious condition and needs to be managed aggressively.There will be increased respiratory rate and chest wall retraction in involvement of lower respiratory tract.That needs to be managed with nebulisation.
I won't get overly worried if there are no signs of involvement of LRTI.

2)Severe cough with posttussive vomiting can be due to infection with some atypical bacteria and that need to be treated with macrolide group of antibiotic like azithromycin.

If cough is severe,causing sleep disturbance and there is vomiting following cough it has to be managed properly whatever may be the cause.
Zedex P contains antiallergic(phenylephrine),bromhexine(to make the sputum thin)and dextromethorphan(cough suppressing agent).Although cough suppressing agent is not recommended in infants considering the severity of cough I would like to continue this medication for another 5 days.
I would like to add salbutamol (a bronchodilator that relieves airway spasm)syrup to relieve the cough.
As there is no specific test to differentiate whether the cough is due to viral infection or due to infection with atypical bacteria,I would like to add azithromycin as benefit of doubt.
Put nasal saline drop and give steam inhalation to relieve the nasal blockage.

I hope this helps.
Please let me know if you have any more doubts.
Wishing your baby's speedy recovery.
Regards

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