Molt is very hard on birds. If they have any underlying conditions, coming back into lay after a molt, or just the molt process is sure to bring them to the surface.
The spot on her neck- is it hot to the touch like an infection would be? Does it look like someone has been picking at her? Could she have bugs that are causing skin irritation? Is her crop OK?
The most common conditions I have found to pop up around molt are- reproductive issues (egg binding, prolapses, increase in shell-less eggs), crop problems (sour crop, stasis), and extreme debilitation from parasites. My flock is healthy, so I don't have to worry about any illnesses rearing up at molt, but a disease positive flock will often have recurrence of whatever disease they are carrying.
I would be checking her for all these issues. I would start by worming her (and the flock). It always a good starting point. A normal worm load that wouldn't affect a bird on a normal day, suddenly becomes life-threatening when molt comes around. Too many resources are being expended during this process.
I hope this helps. I hope you figure out what's going on.
