Can you get pink eye from a handjob then touching your face?

Bacterial "pink eye" More commonly people can get a bacterial conjuctivitis if your partner has an untreated std such as gonorrhea, or even just a uti. Then after handling the genital area, and touching your eyes without washing your hands, you can transmit diseases to your eyes. I have also teated patients who ended up with unusual pathogens in their eyes after oral genital contact.
Anything's possible. Pink eye is caused by the cold virus which is able to "live" on surfaces for several hours after being placed there. The most common transmission is from directly touching the virus and then touching your eye, so it is possible to transmit it if your partner had pink eye and touched himself first. It does seem rather unlikely, though.