A northern scarlet snake?

I found a small snake on a rock in my flower bed. I would say it was less than 12 inches long and slightly bigger around than a pencil. I was looking through the field guide and found a snake that was identical, the Northern Scarlet Snake. The bands and coloring matched exactly. It has a grayish background with reddish bands bordered in black that do not meet under the belly and then reddish spots bordered in black between the bands along the side where they end before the belly. The description, though did not match up when it described it's belly or snout. the description said the belly is white or yellow--what I found had a white and black "checkered" belly. The description also said the snout is pointed, but the one I found is not prominently pointed but more gently rounded. The picture looked exactly like what I found, though. Is this what the snake is? I live in Southern PA. Thanks!