Excessively dry skin patches on my face... any suggestions?

My skin is really dry under my nose, around the side of it up to where my eyebrow starts. I’ve been slathering on lotion all day but it’s not helping. The rest of my nose gets kind of oily, which is annoying. Any other suggestions? I feel like every time I wash my face it makes it worse, but I don’t want the rest of my skin to get bad if I stop washing it altogether. What should I dooo?