The bird is sick, that's not what a broody hen looks like. If its not too late, follow the advice of others, if you're going to give her a shot in the chest, be sure you don't hit anything vital like her crop or any other organ. I'd be very afraid to give a shot to a bird. Look up dosing orally, I did that with mine when she couldn't walk or keep her balance (thanks again Chickenzoo) and she recovered fully and hatched out babies this year. First day I gave her Safeguard, the next five days I gave her a mixture of small amounts of corrid and metronidazole (I just gave her a small amount that looked about right, didnt measure it). Also, kept her on electrolytes, a few syringes of warm water, and baby bird handfeeding formula and kept her in a crate with a light, taking her out for fresh air a few hours each day. Her windpipe was easy to locate and I had a syringe with a tube that I just put straight down her throat to administer all that. She was near death and I suspect she had blackhead.
Good luck, I hope this helps.
-Nathan
ETA: I dont see why she'd need an antibiotic unless she had signs of infection, I am willing to bet its some type of internal parasites or a combination. And mine also fell ill right after I had got her. She's been fine ever since.