Summarize:

Carefully remove the dressing and examine the burn. It should appear less swollen and red thanks to the protective dressing, along with your body's natural healing process. If the burn has a foul smell, blisters have formed, or it appears very swollen and red, go see your doctor. Remove the cling wrap or cotton sheet and rinse off the burn with running water. Then, put on new cling wrap or a cotton sheet.  Apply a small amount of antibacterial ointment or cream with clean fingers to the burn every time you change the dressing. If small blisters have formed, you can apply fluffy, non-adhesive dressing to them or go see your doctor for treatment. If the dressing becomes dirty, wet, or soaked through before the 48 hours are up, change it. The dressing should be clean and comfortable at all times. Manage any pain from the burn by taking ibuprofen or acetaminophen. Follow the dosage instructions and only take the recommended amount. Most minor burns will start to scab over within 1-2 weeks. Try to expose the burn to air by leaving it uncovered as it scabs over.  If the burn does not heal within 1-2 weeks, or blisters form, go see your doctor. Be sure to keep the burn moist while it heals. A moist atmosphere over the wound creates a suitable environment for healing.
Check the burn after 24 hours. Change the dressing every 48 hours. Take over-the-counter painkillers. Allow 10-14 days for the minor burn to heal.