Why does your nose run when you swim?

I understand why you wouldn’t feel your nose running while you’re swimming (because your whole face is wet) but why is it so common for your nose to run in the first place? I’m talking about when you are not sick at all but after being in the water for a while you will have snot coming out of your nose. And then it stops once you are out. Why? And, doesn’t this happen in both chlorinated water as well as fresh or sea water?

Simply because water goes up your sinuses when you are underwater and drains back out when you come out of the water.