Can oral augmentin (amoxicillin and clavulanate) be used to treat "pink eye"?

No: Most "pinkeye" or conjunctivitis is actually viral, so antibiotics are usually not effective. Viral conjunctivitis tends to run it's course in 7-10 days. It can be very contagious, spreading from one eye to the other or to other people. Hand washing is essential. To be certain it is not a more serious bacterial or fungal infection, you should see an ophthalmologist.