My skin breaks out because I work at a dusty place. How can I protect my skin?

Maybe something else. Dust is often blamed for skin breakouts, but there are many possible causes. Let a dermatologist examine your skin, determine the exact cause, and prescribe an appropriate treatment.
Washing. Be sure to take your baths at the end of the day. Avoid baths/showers before going to work as this would reduce the skin barriers to the dust or toxins on the job. Wear long sleeved shirts and try to cover as much of your skin as you can. Otc steroid creams to reduce inflammation/rashes when they occur. If these fail you may have to seek a new job away from the exposure.