If the white aren't affected, I'm GUESSING it's not pink eye, but I'm not a doctor! I would just do warm compresses, but use a paper towel and throw it out each time, then you aren't spreading it from eye to eye. Also, if you take your pinky finger and rub in a circular motion between their eye and nose, that will help it if it's plugged. Try and do that a couple times an hour. I used to do it for a few seconds every 10 minutes with my son...but he had this for almost 6 months. It really helped and I found the more I did it, the less gunk would produce. I don't know if you know this or not, but their eyes are connect to their nose throw a drainage "pipe" and when a child has a cold it will often spread to the eyes, mostely because they can't cough or blow stuff out. I would also run a humidifier in the child's room, to try and make is moist to help relieve some pressure. Good luck and if it gets worse, I would go to the doctor, they do have eye drops for little babies.