Oh, my skin has been so dry lately..ㅜ

Lately, my face feels so hot after I wash my face and my skin dries up so quickly that it's driving me crazy;; I wonder if it's because the weather suddenly got cold..

I'm thinking about exfoliating, but I'm afraid it might irritate my skin, so I can't even touch it. Yesterday, my skin was really dry, so I mixed some face oil in it and applied it, and it's gotten a little better.

What kind of care should I get in this situation? It's really hard to get my skin back in good condition ㅜㅜ