Alun Stick and Alum Stone
It has most probably happened to anyone who shaves regularly. A small nick when shaving with sharp or a dull razor for that matter. The bleeding can sometimes be hard to stop. An effective way to stop it is with alum. Make sure you have a styptic pencil or an alum stone in your bathroom cabinet.
With alum you can coagulate the blood and make the blood vessels constrict quickly. Leave the paper be, and do not go around with small little plasters on the face or neck.