My outdoor cat's red, watery eye with discharge hurts. What can I do?

I'm sorry Cherry has eye discharge. Unfortunately, there is nothing you can do for her at home. The eye is such a delicate and important structure that any eye problem is considered an emergency. That's because leaving it untreated can lead to vision loss. Given she won't let you look at it, it's like very painful to Cherry. I would have Cherry seen by a vet immediately for this, as it needs to be examined and treated right away.