While changing used cat litter I think a piece of litter flicked into my eye, I rinsed my eye with water. Can this cause a eye infection?

Possibly. It depends on how soiled the litter was & how much you got into your eye. If you rubbed your eye & caused a corneal scratch, this may serve as a nidus for serious infection. Rinsing with copious water or eye rinse plus artificial tear drops is probably sufficient. Your own tears & secretions generally protect your eye from infection. But if worsening discharge, vision change, inc. redness: C MD. .