Peeling nose for over a month, and really chapped cracked lips?

I've had a problem for the past month. My nose has been peeling and it's not sunburn. When I peel the skin off, it makes it worse. I don't wear face makeup so I know it's not from makeup. But at the same time as this is happening, my upper lip has been really chapped, red, and cracked. It's a big problem and it's embarrassing. Help!