I have one eye that is always teary (even without chemo!) and I get the dry patches on the outside corner of my eye. I use Tobradex cream and it clears up after 2-3 applications. There are medications you can use to stop teary eyes but I prefer to not take medication if I don't need to. The Tobradex is by prescription but it's an ointment used on the skin so I feel it's OK.