Because of internal dryness in my sensitive, oily skin.

I have sensitive, acne-prone skin that is also very oily. However, due to internal dryness, no matter how much I moisturize, I can't seem to get rid of the tightness deep inside. If I apply too much cream, it looks greasy because my skin is naturally oily, but if I apply just a little, the tightness is really bad. What kind of product would be refreshing to apply to help with this tightness? I prefer something oil-free.