Yes it definately does! I've had a couple of eye infections since my bean was born as they come on when I am tired...! I simply popped a bit of milk on each time I expressed (so for you each time you feed) and it soon cleared up. Especially important to pop it on at night so that the anti bodies can work. I've also used milk on cuts, grazes spots and burns - all on me not the baby!
Make sure that you get rest too to give you a chance to fight the infection. Feel better soon.