I would never put anything else in my eye that wasn't specifically meant to go there.
I don't suppose even a saline rinse would help, since capsaicin is oil-soluble, not water-soluble.
It goes away pretty quickly. It hurts like !@#@#$ until it does, though.
As far as getting it off your hands, use an industrial-type hand scrub. Act like it's (odorless) 90w gear oil and it'll come off.