Severity of my cigarette burn? Should I to to a dr?

I got a bad cigarette burn on my face. I remember it hurting a little, but I was incredibly drunk when it happened. The next day i rubbed some of the black skin off in the shower, and now (2 days later) its about an inch in diameter with the middle white, and the outside very red. I doesn't really hurt at all, even to the touch. I've kept it soaked in neosporin and covered with a band aid 24/7. How bad is it, and will it leave a scar, and should i seek medical attention?