First of all, don't worry. After all, it's not a big deal. However, you are supposed to have a understanding, eyes are the most fragile place of our body, but don't rub your eyes with your hands, otherwise it will cause damage to your eyes. Therefore, you have to adopt the following methods on the premise of washing your hands totally. There is a simple way, washing them with flowing and clean water. Thus, the papercut may get out with the flowing water. If it does not work, using the fingers to pick it out in front of the mirror, this might be help. And then, you will feel better. In a word, I wish these suggestions could give you a hand more or less.
It is not normal. And the papercut may hurt your eyes by hurting the corneal which is so weak. You'd better get it out of the eyes with the fingers. Then you'd better use the warm compress to make the eyes feel comfortable. In addition, you could also use some eye drops to eliminate the bacterium in the papercuts.