Whenever a finch is looking 'off', the first thing I do is put them into a small hospital cage (so they don't waste energy flying around in large spaces) and put a heatlamp on one side of a perch so they can go to it if they need the warmth but still move away from it if they don't need/want the heat.
For a possible eggbound hen (sounds like she could be), I give one drop of Liquid Calcium in the beak and then add some to the drinking water as well. Make sure she has water, seed and eggfood available on the floor since they usually cannot fly well when they are eggbound.
You can also drape a wet towel (soak it in hot water and wring it out so it isn't dripping all over your floor) over the top and around 3 sides of the hospital cage (not touching the heatlamp!). This is for much needed extra humidity.
Good luck!!
