Gooey eye & breastmilk....

[The[cookie]Doctor]

Alex's gooey eye didn't clear up until he was about four weeks old.
As well as the breastmilk you could try massaging near the tear duct.
Use the tip of your pinky and massage between the eye and the nose (DYKWIM?) for about thirty seconds. I tried the BM for ages and it didn't work, (would clear up for a day but come back) but the HN massaged the tear duct and it worked a treat.

ETA: Didn't see Sushee's post before i posted.