An avian vet isn't necessary to run a fecal. Any vet can agree to do it. The issue is finding a vet to agree to do it as many are high and mighty about treating chickens. Assure them they need not treat your chicken, just run the float test on the poop and tell you what's in it.
Have you given her a thorough exam head to toe? Look inside her throat, as well. Part the feathers and look for anything not supposed to be there.
It wouldn't hurt to collect a poop sample and have your vet run a fecal float for parasites.
By the way, hens eat oyster shell when they get a...