My burn doesn't swell but its brown colored?

I was doing my research about my hot curling iron burn (I accidently hit my neck for a second but the setting was on high) , and the description matched a third degree burn. Sort of. Its a very small area (less then a quarter size), and at first, it was redish. I didn't do anything and after a day it became brown. There's no blistering or swelling, and it only hurts a little to touch. I've just left it alone, what degree burn is this? And will it leave a scar?