Yellow Eye gunk after naps.

Once in awhile Lilly has yellow eye gunk lately from her left eye after sleeping. I clean it up, but for a few days it wasn't there at all. I saw it yesterday, but we have a vet appointment May 10th for their rabbies shots, so I'll ask then. I wanted to know if anyone had the similar thing happen. I read it could be conjunctivitis. WIlla had it a couple times after sleeping too in her right eye. There is no swelling or puffiness around the eye, or redness on the eye ball. 

They don't itch or paw at their eyes, and just me being a worrisome dad! haha

My Grayson recently had some green oozing from his left eye. Our vet says most likely it's herpes for him and we are doing some eye drops as well as lysine supplements. See what your vet says. Anything with the eye needs to be checked out.