When using the brush tool on a mask, it is painting black and white rather than burning and dodging

Hi Brie, based on your attached example, you have a layer selected. What you need to do is select the mask and paint black or white on that mask. 

If you use a layer for non-destructive dodge and burn, then you have to change the layer mode to ‘Overlay’.

To "paint" on the mask, you will need to select the mask instead of the layer directly. To do this, click the secondary thumbnail next to the main layer thumbnail in the layer panel. You'll see the little outline around the main thumbnail for your layer jump over to the secondary (probably white) thumbnail that represents the masking layer.
Pro tip: If you want to see what the masking layer actually looks like, you can alt(opt)-click on that secondary thumbnail and it will show you the mask.

One other observation is that the layer mask that you currently have, is white. This means that whatever is in that layer would be shown and it would cover what's in the bottom layer. Unless, I'm assuming wrong and the layer you want to mask in, is the topmost layer. In that case, you'd want to add a mask on that layer(again assuming that this layer has the tongue and you're trying to mask in/ out some of it?). Remember, white reveals and black conceals. One more tip. If the entire layer mask is white(such as yours), select the layer mask then hit CTRL+I to invert it, making it black. This will hide the contents of that layer. Then you can paint with white on the mask to reveal the tongue.