It is not a big problems, But you shall use clean water to wash them out immediately.
Technically, the shampoo will hurt you eyes. If you are use medical shampoo, it usually harmful to your eyes. Anyway, for the sake of your eyes, you shall wash your eyes with clean water. Maybe it is a little hurt to your eyes at the beginning, the symptoms will fade away for a few minutes.
If the shampoo comes into your eyes, you timely rinse your eyes clean; it may not harmful to your eyes. If your eyes are still painful on another day, you should go to the hospital to have an examination, you can have some anti-inflammatory drugs and use some eye drops. so you don have to worry about it so much.
Yes, it would, but it depends on what kind of shampoo you use. Shampoo is a daily hair care product, which removes dandruff, oils, dirt, skin particles and other particles that build up in hair. The main integrations are surface active agent, conditioner, smooth agent and essence. Hence, there are two main shampoos that are used in daily life. One is chemical shampoo, the chemical integration would be harmful to eyes, especially the cornea. It's better to clean eyes with cold water immediately if it happens. The other one is herb shampoo, it might not be harmful to eyes.