Artificial tears are the best over the counter eye drops for eye infection. But it can only lubricate your eyes. It can't clean up the bacteria or viral in your eyes. So you'd better choose the eye drops which are suitable for your infection. I suggest you to see an eye doctor first.
If your infection is not very serious, you can apply some ice or chill cucumber pieces on your closed eyes. The water from the ice will flow into your eyes and remove the bacterial and relieve the inflamed part. And the coolness will make you feel better. You can have a try.