I am usually anti powerful drugs to start with, and prefer to go the holistic way first.
Except when it comes to eyes.
I guess it comes from having had a Pekingese who had a corneal scratch that quickly turned into an ulcer in a couple of days. When I ran to the vet, I felt terrible for not having gone sooner.
As for eye goo, if it is an infection it can get bad quickly. The eye is warm and moist, and bacteria just love that environment.
So I would go get it checked. Just in case.