I was cutting chicken raw chicken and a drop of juice splashed in my eye. I tried to rinse my eye well. Can I get salmonella or infection?

Skin is strong. You have to ingest the bug to get infected. The lining of the eyes is like your skin. It sounds like your risk is minimal or zero.
Possible but rare. you are more likely to get in infected from your hands, kitchen utensils, etc that have not been thoroughly cleaned and under cooked chicken.