I sure hope Corkscrew gets better soon.
My RB Pepper had a clogged tear duct so his eye ran all the time. Unfortunately there wasn't anything that could be done.

Sometimes I notice that one of Cirrus's eyes will water but they're never red. I've heard that this sometimes happens when they use the litterbox because they try to be very clean and dig a lot to cover up their mess so the litter may be irritating their eyes.