Sounds like she has a slight prolapse or swollen vent. What are her droppings like? When I see this, first thing I do is separate the bird so that the others don't pick the vent. Second thing I do is start checking droppings - looking for diarrhea, loose droppings, any mucus, any red. Third thing I do is clean the bedding, the feeders and waterers, and make sure everything is ultra dry and clean. And then I feed a probiotic, usually plain yogurt. For her age, 1 teaspoon per three chicks.
You can feed it straight, or mix it with as much water an dmix that with an equal amount of crumbles. Let sit until the water absorbs, 10 minutes. Then if it's goopey, add more crumbles. Feed that to them after withholding their feed for 20 minutes (the making time). Make sure they all get some. If some eat more than others (and note who they are), then remove them from the brooder to a little cardboard box til the others get their fill.
The yogurt provides living bacteria that can help with intestincal/cloacal irritation. Usually birds this age prolapse because of diarrhea or digestive tract irritation, and often enough it's because of coccidiosis.
I'd want to rule out coccidiosis (watch her droppings as you have her in her own good little sick brooder). If you see diarrhea, then treat her with Corid (it's stronger amprolium). If you absolutely cannot find Corid in a day, you can use Sulmet - but it's more harsh as it's also an antibiotic. Are these babies eating medicated (with amprolium only) chick starter? No grains? Just mostly crumbles?
Incidentally, it might also be that she's being bullied away from the feed more often than is healthy and that she's gone light. The lightness and weakness could also cause the prolapse and digestive irritation. If her droppings are pretty solid but dark colored, are dark green if you smear them against white paper, then she's not getting enough to eat. Then you'd want to make two brooders - one for the tougher more vigorous chicks, and another for the more slow or delicate birds. Feel them - pick out the light weights - brood them separately.
Give the light birds yogurt for a week, then all of them can get it weekly through their 'starter" weeks (weeks 1-8), then occassionally til 5 months. as they're eating "grower" ration. Then when the pullets' combs start to redden and enlarge, you slowly integrate layer, oyster shells free choice, and give yogurt once a week til everyone's laying.
I do look forward to hearing your replies so that hopefully we can help you out.
p.s. If she won't eat on her own, make a little damp mash - like above, just about a 1/2 teaspoon, and add a couple of drops of honey, karo syrup, or something therelike - maybe some cooked oatmeal. (Grind the dry oatmeal into a powder in the food processor first, then cook it so you don't need grit.) To whatever you get her to eat, give a little of the yogurt and some of the karo or whatever. You might need to hand feed her and dribble a little water at the side of her beak at first if she's weak.
Make sure they're all the right temperature. First week is 95, second is 90, third is 85 - no lower, not even at night.
