My son had the same problem with Pink eye. It seemed once we got rid of it, it came right back. Children can get it from themselves as well as other children. If a child has a runny nose or sneezes and then uses their hand to wipe the nose and at a young age this is common. They will wipe the nose with their and and go from the nose to the eyes and pink is caused that way too. If you know that pink eye is starting there is a eye drop you can buy over the counter no. I'm sorry I don't remember the exact name of it, but it has a pink cap, is a very small bottle and usually on the top shelf. It is by other childrens cold items. the box does say pink eye on it ( I believe). I always find it at wal-mart.
Good luck I hope this helps.