Especially for people with sensitive skin, laundry detergent and dryer sheets can irritate the skin. Some people even develop contact dermatitis and mistake it for acne. Swap your usual soap for fragrance-free detergent, skip the dryer sheets, and this could clear things up.
Acne Culprit: You're Allergic to Laundry Detergent
Source: Flickr user Invernodreaming