Dry skin is not uncommon (in older birds and certain climates).. it's a good reason not to use DE if you are.
Angry red skin is a whole other story. Feathers missing around the head (as described in this instance) can *often* be from flock members pecking to get into the occupied nest box.. trying to make the sitter get out.
Do you have a rooster? Did she molt a previous season?
Have you confirmed she's actually broody.. is she clucking, puffing up, screeching and stuff? Do you want any eggs hatched or have room for more flock members? What size is your coop and run, how many boxes, how many flock members of what gender?
An egg bound hen won't be coming out to eat and drink.. those are both good sign. How long has it been going on that she started staying in the nest box?
Chickens are Stew Pidassos.. when it comes to pecking order and it can get brutal.. sometimes, that's just what it means.
2 seems a little old to be broody for the first time (not unheard of).. has she been broody before or is this a new behavior?
Are you able to post pics?
Please note, all my questions are in attempt to understand IF there is anything more you can do to help her or cause for concern.
Hope all is actually well!