It sounds as though you have a combination sensitive skin type. If your skin is dry and it is not receiving adequate moisture it will respond with rebound oiliness. You may find relief in focusing on the following ingredients in your skin care regimen:
When choosing a cleanser, select one that is fruity acid based. These ingredients are known as polyhydroxy acids. They work through gentle chemical exfoliation while attracting moisture back into your skin. Use this as a three minute mask and it will clear the blackheads problem. I wouldn’t recommend using an intense exfoliator as this will only irritate the oil glands further. Follow your cleansing with a polyhydroxy based daily moisturizer and avoid vitamin E, as it could provoke further congestion.
Apply a non-comedogenic sunscreen afterwards and control any excess moisture later in the day with a matifying serum.
At night you can use your cleanser in the same manner once again and then follow with an antioxidant serum. Allow this to soak into your skin for three minutes before finishing with a moisturizing night cream, preferably one based around vitamin B5 and hyaluronic acid for moisture enhancement. Retinol or vitamin A can be introduced later to clear up the pimples, but this can dry your skin out further and should only be added under medical supervision, and after your moisture balance has been corrected.