My skin is such a problem. First it's red and dry, then it gets oily. How can I deal with my combination skin?

A lot of people who get oily skin feel the need to strip off all the oil. But all that does is make your skin dry - which makes your skin produce more oil in response.

First, stop using any products you have containing salycylic acid, lactic acid, alcohols, triclosan (antibiotic), bar soap or similar chemicals, and stop wearing makeup for a while. All of these can make your skin very dry. Since your skin is red, it's probably irritated, so stop using exfoliants for a while so it has a chance to heal. Once the redness has gone away, you can use a gentle exfoliant, but don't scrub! Use lotions designed specifically for the face (I recommend Oil of Olay formulas for sensitive skin). Oil treatments like avacado, tea tree, almond, etc. are also beneficial and gentle, as are cucumber face masks.

If you have acne, don't touch your acne products for a while, let your skin heal, and see if the acne goes away by itself. Often it does.

Don't wash or moisturize your face too often, even with just water. Once or twice a day is enough. Also, try not to touch your hands to your face, because your fingers can deposit extra oil. If you give it a little time, the excess oil should slowly go away.

If these treatments don't seem to be effective after you've tried them - give yourself six weeks minimum - go see a dermatologist.

It all depends on the kind of facial cleanser you use and if you use facial lotion.
If you have acne, I would use an OTC acne cleanser of your choice for oily skin, then use a facial lotion that contains salicylic acid like clean & clear daily mosturizer w/salicylic acid. Make sure to use that lotion right after you wash your face.
If you don't have acne, then you can use just a daily facial cleanser for oily skin and a daily mosturizer.
If that doesn't work, you can try a facial cream cleanser, and then you don't need lotion. I know they do have facial cleansers for combination skin, sounds like what you have. Just go to walgreens and look at the facial skin care section and read the labels. Hope this helped!