Maybe the moisturizer isn't working for your skin type?
Try cleansing and moisturizing with coconut oil before bedtime (don't use soap). After about a week, the natural oils in your sebaceous glands will be stabilized and any blemishes / acne / blackheads reduced

CO absorbs VERY deeply, and is kind of a magic cure-all for skin problems even oily skin (overactive sebaceous glands). It won't clog your pores. I use it as a facial cleanser / eye makeup remover / moisturizer.
If it's still dry when you get out of the shower, you can use just a little bit (maybe 1-2 peas worth) and it will make your skin glisten without looking weird.