Depends. Generally it is acceptable to shower and wash the area gently with a mild soap. Don't use alcohol, betadine nor hydrogen peroxide. Then apply some type of a dressing to the burned area. Do not leave open to air. Check on your tetanus status.
Superfast healing. The real question is what not to do that slows down healing. Avoid using alcohol, peroxide, hibiclens, betadine, and bleach solutions. Inflammation (red, hot, swollen, tender) is important to healing. Cover the area with a clean dressing changed every other day and protected from trauma. Antibiotics do not help healing unless it is truly infected. Showering is ok but go easy on the scrubbing.
Controversial. Many doctors do not let their patients shower. If you are using xeroform or silverdine, you can shower daily or multiple times a day, as long as the water goes from the burn down. Then put a dressing on as clean as possible. You should never bath with a burn. Bacteria from the genital and rectal area can infect the wounds. You must consult your doctor and follow his/her instructions.
Aquaphor. Topical aquaphor can offer relief from symptoms such as burning and irritation of skin.