I also had oily skin with dryness on the sides of my nose. You can try a medicated skin care system if you have a lot of acne. Or, a combination skin system may work for you if the acne is not too severe.
The main thing that helps me, though, is to only use a nighttime moisturizer on the dry skin area around the nose and not on the rest of my face. In the morning, I use a day moisturizer for my skin type and find that's all the moisturizer I need.
Most other people need a nighttime moisturizer though, so you may need to experiment.
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