Paper cuts often occur on your fingertips, which are extremely sensitive (many nerve endings). You also use your fingers a lot, so you disturb the cut often, which really hurts because of the exposed nerves.
The best thing for a paper cut is tea tree oil. It almost seems to seal up the cut. It kind of warms the cut & soothes it right away. I won’t be without it. When I was working, everyone would come to me for some when they’d get a cut. It works!