Juno, my 10 mo. feral is a very good groomer, except for her eyes. She gets this gunk on the outside of her eyes and it doesn't seem to bother her. I tried a wet cotton ball and she doesn't like it too much but let me do it for a while and then had enough. She is not agressive, but when she tried to get away I knew it was enough. She won't let me pick her up so I need to bend to her level. When I first got her her eyes were running but the vet said it was ok & normal. Her eyes don't run anymore except for this discharge that sits on the side of her nose by her eyes. Really ugly and I'm concerned about her skin there. Would appreciate any advice.

I would have her checked out. She could have a mild upper respiritory infection going on, just the remains of something from when she was younger. I'd see if you can get the vet to give you a course of antibiotics.
If it doesn't respond to antibiotics your cat could have herpes, which just means that if your cat gets stressed out she may have "cold like symptoms". Goopy eyes, runny nose, sneezing etc.