2nd degree burn

I believe I have an oval burn about an inch wide and 3-4 inches long on my arm just above the wrist. (I don't remember but I believe I must have touched oven while removing muffins or dinner)  I know it didn't hurt enough for me to make note of it ... so no immediate wound care. When I first noticed, my skin was discolored and somewhat swollen with red skin surrounding it ... but it didn't hurt.  When I washed it, a thin layer of skin came off revealing the area below as moist and creamy white. Cleaning the wound hurt some.  So I left it uncovered to dry out and heal.   After 3 days the red skin surrounding the burn was increasing but it did not hurt.  I put a triple antibiotic ointment on and applied a large bandaid. 2 days from applying the initial bandaid I needed a larger bandage. Now its 5 days from initial bandaid, the wound looks almost the same as when I first put on the bandaid.  It still doesn't hurt. (I admit I have high pain tolerance) Should I leave it exposed to the air so it dries out?  I have health insurance but don't want to bother my doctor with something I can care for at home.