if it is actually Pink Eye no.. and there are no otc remedies for it.. it is very contagious as well you should see a DR asap to get drops to cure it. These are your eyes we are talking about here.. *never* take any risks with them.
If it's really pink eye (conjunctivitis) it won't go away by itself. You need prescription medication for it and it's highly contagious. Some things look like pink eye but aren't, like allergies or a tear duct clogged with an irritant. You can try to gently clean the area with a clean washcloth soaked in warm water, and use OTC eye drops. If this doesn't lead to obvious improvement in a few hours get to a doctor or walk-in clinic, and stay away from people.