It seems that contact lenses care solution can be used for pink eye and it is recommended by some people. The solution is mainly composed of sodium chloride, water, aseptic. Different product is made with different prescription. To treat your pink eye, first of all you need to choose the solution which will not cause allergic reaction. Mild solution would be better. Choose it with boric acid, which would effectively relieve the swellling. Pour some solution is a clean cup, and blink your eyes while the eye is sinking in it. Blink more to ensure the solution lubricate and rinse the eye completely. Use a different cup for the other eye. It sounds weird but it iis true. Doctor always recommend saline water for pink eye. The component is nearly the same with contact lens solution. But the care solution contains some disinfectant, anti-fungal and anti-bacteria agents in it as well which make it more effective than just saline water.
No, the contact lenses solution will not kill the pink eyes. It can kill the protein which is sediment on the surface of the contact lenses. The bacterium of the pink eyes should be killed with the eyes drops with anti-inflammation. You should not use by mistake. If you have the pink eyes, you'd better not go out often because of its contagious character.