My experience with conjunctivitis ("pink eye") has been this:
A child came to my home daycare and his parent said his eyes were goopy and swollen when he woke up that morning. His eyes seemed alright throughout the morning, no discharge, not red. Then he napped, and when he woke up there was a greenish discharge from his eyes that continued all afternoon, and the whites of his eyes got progressively redder. He went to his doctor that evening, was diagnosed with conjunctivities, and he took antibiotic eye drops for about a week. The doctor said that pink eye is contagious when there is discharge. Not surprisingly, another child at the daycare developed the exact symptoms/diagnosis a couple of days later.