Well, generally speaking, if there is a little sweat getting into your eyes, it can not lead to pink eyes, unless your eyes are extremely sensitive than other people's eyes. So you do not need to worry about it. For your situation, you just need to wash your eyes carefully. And then it will be fine. And you should know that pink eyes are caused by irritants, such as bacteria, allergies. So just pay more attention to them.
Well, as you can see, pink eyes are resulted from multiple reasons, which made it very complicated sometimes, so, it is true that excessive sweat in the eyes could give rise to some problems, and if you dare to rub your eyes with your dirty hands, you are very likely to have pink eyes. Anyway, sweat contains some dirt and dash, as well as bacteria, which could generate pink eyes.