I've been using The Body Shop's Tea Tree Oil to control some of the more painful blemishes lately. This product was stated to "help clear blemishes quickly and effectively without over drying the skin." If you have dry skin and you develop acne, perhaps instead of drying it even further with some of the strong acne cleansers out in the market, maybe you can try applying some Tea Tree Oil!
Why do people with dry skin still develop acne? The skin tends to produce more oil in response to dry skin. So to prevent that from happening, we moisturize!
Tea Tree Oil, unlike other oils, does not clog pores. Instead, Tea Tree Oil contains many beneficial medical properties when applied topically. According to Wikipedia (link), it includes antiseptic, antibacterial, antifungal and antiviral actions.
Unfortunately, nothing ever works immediately/overnight. In fact, this treatment works quite slow in general to dissolve that damn blemish. It is, however, soothing after you apply it and reduces the redness and inflammation initially.
The Body Shop's Tea Tree Oil is diluted so you can apply it directly onto your skin. So essentially, it only contains 15% of Tea Tree Oil. If you find that you need something stronger, you can always try to get 100% Tea Tree Oil from the drugstore and dilute it yourself. It's a good thing to keep around for insect bites too :)