Hello,welcome to HCM,
First of all don’t worry and understand what is happening .
1.the tears from eyes drain from tiny pores at the insides of lids into the nose .
In this passage near the junction of eye and nose is a sac which holds some tears while on the way to nose.
This sac is sometimes blocked /partly open in infants. it leads to watering and sticky white discharge from the eye.
You need TO DO THIS;
1.keep cleaning as you are doing
2.
massage the sac ares with a clean index finger with upward peessure to remove all mucus through the sac ,wipe clean ,put antibiotic drop(tobramycin/
levofloxacin) by pulling lids apart.
Redo massage with downward pressure toward nose to facilitate tear
drainage .
Follow this 7-8 times a day ,baby will cry but keep at it.
You must see results in a week/15 days. Some cases take longer .
If it doesn’t stop by 3 months visit an eye specialist who might open the pore/track to the sac with a small probe.
hope i have put your worry at rest.happy to help