I suspect that bringing the new chickens home also brought home some "bug". Alternately, it could be that the new chickens in the barnyard caused a bit of a pecking-order change and there might be an injury.
In any case, I would get saline eye wash or sterile eye wash from the drug store and clean out the eye thoroughly. The eyes drain into the choanal opening (cleft in the roof of the beak) which in turn drains into the digestive tract. The drainage (which might contain bacteria) will drain into the digestive tract. So to prevent secondary diarrhea, I would give him some probiotics. In fact, I'd give that to them all because of the stress of new birds. You can use plain unflavored yogurt (as long as you're not medicating with -mycin or -cycline drugs), or you can use a prepared probiotic like acidophilis capsules from the vitamin section of the pharmacy or some grocery stores, or Probios brand dispersible powder found at many feedstores.
Whichever probiotic (living bacteria - not a medicine) you choose, add it to smoething that the bird will eat quickly as a treat. Eggs, the powder sprinkled on bread, the yogurt mixed with a little water and then mixed with crumbles and left to set til it absorbs, etc.
On the eye, if you can get a small tube of Terramycin Ophthalmic (eye) ointment from the feedstore or a vet (it's over the counter) then I would use a small "ribbon" of that in the eye daily. Clean the eye about 10 minutes before medicating to remove the gunk, then put the ribbon on the bottom eyelid's shelf so that it melts into the surface of the eye.
If you're not seeing any more respiratory symptoms, and picking him up and listening carefully to his breathing reveals no rales, wheezing, hiccups, rattles, or 'snicks' (small cough/sneezes) you might get by with just boosting his immunity and treating the eye topically.
To be safe, I would pick up a package of antibiotics while at the feedstore. Duramycin is ok, Tylan and LS50 are fabulous. Sulmet's another good one to have on hand for its effectiveness against Pasteurella and Coryza. I don't believe this is that - just some respiratory something or eye injury.
Some birds also get what is colloquially called a "one eye cold". And there's also "eye worm" to consider. Really it's nearly impossible to tell without further investigation. But in all cases, buying a small bottle of VetRx at the feedstore (even the rabbit version, or Marshall Pet's Peter Rabbit Rx from
Petsmart or
Petco) will help somewhat. When I have a bird with an indistinct eye issue, possibly respiratory, I will use diluted VetRx on a q-tip and swab the roof of the mouth where that opening is. The fumes to into the eye's sinuses. It also helps the chicken to breathe better in case there's something respiratory brewing. It won't harm if there is an eye injury alone. I would use the terramycin in the eye, but the VetRx to clean the nostrils and that roof opening just in case. One bottle (2 ounces) lasts ages as you usually dilute it.
In fact, I used that this year when I brought home some new birds and one bird developed a bit of a swollen conjunctiva of the eye and sneezed once. I treated as I've described to you and never saw another issue with it.
As for the vent and cloaca (the rear end and the anus/reproductive opening), you'll want to check the bird carefully for mites to rule them out. They're nearly microscopic, and they only get on the birds some nights, so check at night a few times this week - with aflashlight (and the coop lights on) to help you find them. Check every inch of her body.
She could also have 'vent gleet', basically a fungal/yeast infection. That can cause problems including vent reddening, irritation, and feather loss. Feeding her and the others the probiotics can help with this.
Giving them all some organic apple cider vinegar in the water will also help if there's a yeast/fungus issue inside due to bacterial inbalance or a nasty environment where she came from before the flea market. It might also help if your eye-sick chicken has excess mucus in his throat. 1 teaspoon OACV (organic only for the bacteria in it please) to 1 gallon of water. It compliments the yogurt's or probiotic's activity, helps correct gut acidity, helps them digest their food better, and helps them be more thrifty. I'd do it every other day this week, then just weekly or monthly as a "tune up" along with the yogurt.
In the old days, they used to recommend feeding milk products to chickens - but in the old days, they weren't pasteurized clean of the lactobacilli in the products. Now, they do clean them of bacteria - but they replace those bacteria into yogurt which is why birds can eat a little (1 teaspoon per bird) without problems, and with good effects instead.
Just watch the young one - separate him just in case, keep him warm, make sure he eats as a lot of their feeding drive is visual. Then let us know if you see anything different or any changes.
