Sounds like what my cat has. Sometimes black gunk can build up in the corners of their eyes because of allergies or simply just daily use (think about our eyes full of sleep when we first wake up). Sometimes cats are born with congenital deformities to the tear duct, not harmful at all, it just causes one or both eyes to tear up and collect more than the usual gunk.
Just clean out the black stuff with a moistened tissue and keep an eye on it. If it continues but doesn't get any worse just keep cleaning it on a regular basis. If it gets worse and he begins to cough with his sneezing seriously consider taking him to the vet for a check up. It could just be a cold but you'll want to know for sure!
What did you do MURDERER
a home remedy is your finger, its just dried tears, hold the head and scrape lightly downward, dogs have it too, get rid of the crud, and he ll thank you ! its like u having a big booger you cant get out by urself !
I hear you, I am a student and understand the unwanted expense. You can clean away the gunk and closely montitor your at. It is very possible that it is a cold. I always wash my hands wen I come inthe house before touching them. Pay attention to how active he is. If it has already been a week and he is just sleepng a bit then wait it out. If he is slowly getting lazier take him in. You can try calling the ASPCA and seeing if they have help with medical expenses.
Either way a call to the vet couldn't hurt