I had that problem maybe a month ago but because I overwashed it trying to get rid of blemishes but they ended up getting worse and with dry cracking, flaky skin.....
You have to exfoliate to get rid of dead skin cells so I couldnt stop exfoliating so I stated exfoliating less harshly and more gentle exfoliation. I moisturized my skin with thicker lotions made specially for dry faces and did it more often. I kept reapplying all day whenever it started losing moisture. My lips werent horrible but they were cracked and dry so I rubbed olive oil on them and again kept caramex on them. But the one where you put it on with your finger one cause that one is more thick and the other caramex are more glossy
But what I think helped out my dry skin the most is water. I drank TONS of it. No kidding I would drink it all day. I would sip it once in a while but I would take big drinks all day. Its true what they say about water it does great things for your body. Appearance wise it cleared my skin so it was moist and blemish free and just great skin overall.. Hope I helped you a out a bit and GOOD LUCK!!