Thank you for your query.
It is not unusual for children of this age to contract upper respiratory tract
infection frequently and more so when they start going to school. Your son has contracted an infection from the school and must be running low because of this. Kindly see if he has fever
and give him some cough
syrup. In case the problem persists then you need to consult your doctor.
Though the chances of transmitting the infection to your 3 month old baby are there but the inherent immunity shall protect the 3 month old baby.
I hope I have answered your query to your satisfaction.
Wishing your son an early recovery.
Rajiv K Khandelwal