I am really sorry that all family members are suffering from cough
. Since multiple family members are suffering, gooey eyes is present in children its probably a viral chest infection
. Respiratory infections due to viruses usually resolve on their own without causing serious problems. Antibiotics are justified only if there is fever
and evidence of pneumonia
like breathing difficulty.
Cough can be really disturbing which can persist even weeks. Don't start cough medicines on your own especially for a child less than 6mths. Get a doctor's consultation who will decide the need for cough suppressants.
Don't worry, there is no one who don't catch cough and cold. Its going to be alright soon. Take care.