Symbolism, Imagery, Allegory
Nancy's hands are mentioned several times, indicating her increasing madness. When the kids are at her cabin, she leaves one hand on the hot lamp. After taking it off, she "stood there, looking at Caddy, wringing her long hand as though it were tied to her with a string" (4.13). She apparently doesn't feel the pain. She also leaves her hands in the fire, also while the kids are at her house (4.20).
OK, yes. This is pretty erratic behavior on Nancy's part. The primarily rule of hot surfaces is do not touch the hot surfaces. The secondary rule of hot surfaces is do not touch the hot surfaces. The third rule is do not talk about Fight Club. Nancy is acting madder than a hatter.
But let's think about what she's doing here, besides riding the fast train to HandBlistersville. She's compromising the attribute of herself that is, in the white family's eyes, the most useful. She's hurting her hands, which do the laundry, cook, clean, and generally give her Cinderella-like superpowers. Man, those are lame superpowers.
This is, on the one hand, a dumb move. She's hurting the part of her body that helps with her livelihood. One the other (burned) hand, this is a brave, desperate and extremely rebellious move. She's hurting the only part of her body that her white employers view as useful.
If you've seen the 80's masterpiece Ferris Bueller's Day Off, you'll remember Cameron's desperate stand at the end of the movie—he destroys his father's beautiful Ferrari. This is because his father loves the car more than he loves his son: Cameron wants to highlight his father's messed-up priorities by destroying what he cherishes the most.
Nancy's doing the same dang thing. Her white employers don't value her… they value her as a useful set of hands. So in a rebellious (and unaware—she's kind of out of her mind at this point) act of self-destruction, she sets out to screw up her hands.