I wouldn't recommend using the burn tool for anything. It is a sledghammer tool, and it doesn't allow for undo.
Create a burn/dodge layer by adding a new layer (not adjustment) and filling it with 50% gray. Set the blending mode to overlay - or maybe for here, soft light. Set your brush opacity to 4-25 and paint with black or white. Black burns, white dodges, as you would imagine. It should be the last (top) layer in your layers - the last thing that gets applied, after any other adjustments. That's if you want to doge this out.
You would also create a gradient mask for an adjustment layer, if that fit. That would be preferable to attempting to paint it by hand, imo.
Lenny