It is very possible to get pink eye for sharing eye drops. There are totally three types of pink eye, which can also called conjunctivitis, bacteria, virus and allergy.
Sharing eye drops with a conjunctivitis patient might let the secretion of the pink eye into healthy eyes, which will lead to infectious eyes. Try not to come into direct contact with conjunctivitis patient. If the pink eye is caused by viruses, it would be very infective, and even one looking at the eyes might make you get pink eyes (when I was little, I always heard this kind of sayings). Don't use your hand to rub your eyes. Pay attention to eye sanity. Eye drop can only be used by one person. Never share it with anyone else to avoid any infection.