What to do for kitten eye infection?

We are watching a stray kitten for a friend while she is out of town. We have been feeding it kitten milk replacer and kibble and water. It is about 6weeks old. It has an eye infection where it's eyes stay shut after it sleeps and we have to wet them with a warm cotton ball to get them to open. The third eyelid is also visible. What can we do at home to treat the infection?