I am not sure if this is good for a 2nd degree burn or not. But do you have access to an aloe vera plant? When I was young and worked for Domino's Pizza I burned my arm on the oven door. My manager broke off a piece of this aloe vera plant and rubbed it on the burn. It hurt like the dickens but it didn't scar. I also know that you don't want to expose the burn to the sun at all.

Hope that helps a little? *shrug*

Denyce