Thank you for your query.
An infant can pass motion a number of times if he is being breast fed which I presume is the case with you. Breast fed infants can demand a feed every hour or so which is very normal in the first few months.
Your son will be having a upper respiratory tract
infection if he is either sneezing
or coughing or is having copious mucus secretions from the nostrils. This does not appear with your son's case. As he is having watery, red and puffy eyes, he may be suffering from conjunctivitis
for which wipe his eyes frequently with luke warm water. Anti-bacterial eye drops may be required if there is purulent eye discharge.
I hope I have answered your query to your satisfaction.
Wishing your son an early recovery.
Rajiv K Khandelwal