There may be so many causes for cough. Ear infection
is common during cough and cold, as there is collection of some fluid due to improper drainage
This cough may be infective or noninfective (allergic).
Cough may take time to subside completely even after proper treatment of infection.
As there is sibling history allergic cough
or cough variant of asthma
must also be ruled out.
Cough type depends upon the site of involvement. It may be barky, brassy whooping depending on the etiology.
So I would suggest you to consult your physician for further evaluation and management.