Do you know what a broody hen looks like? In the nest box, grumpy/growling, puffed up ect. If she is broody- when you take her out and put her on the ground- they usually will walk around puffed up, making angry sounds, wings down, neck puffed up, then poop/run to the food/water and gobble some, then run back to the nest box. A sick hen who is seeking shelter in the nest box will not usually act angry when you take her out and then run fast to poop/eat/drink. Sick hen in likely to just stand there or sit down, maybe walk slowly around being lethargic.
If you determine she is broody- then either give her eggs, or look up 'breaking up a broody' if you don't want her to occupy the nest box for the next month.
If you still think she is sick, then you need to take her out and inspect her head to toes (including vent, crop, keel) to help determine what is wrong with her. Also replying with lots more info about her would be helpful (age, how long you have had her, eating/pooping?, what do you feed? ect)
