What is happening to my cat's eye?

(Imgur upload because reddit won't let me upload the picture on here for some reason)

Her eye has been like this for about a month, it kinda looks like a debris from the tear duct was spread across the eye. However, I've been cleaning the eye often with a damp, soft rag and while it helps to clean some of the stuff off, her eye is always left with a concerning amount of the supposed debris. I'm not even sure if its debris, but whatever it is it doesn't want to come off. She doesn't seem to be in any pain though, but it looks like the eye is progressively getting worse. I don't have enough money to afford the vet, so I need an at-home solution. Any help would be VERY appreciated.