Neomycin is NOT the right med, no. You don't need a vet for this. In fact, most know nothing about chickens anyway.
Take the med back and educate that employee about coccidiosis. Tell them a breeder told you that NO antibiotic is for cocci, that it is caused by a protozoan, similar to what would cause intestinal distress when a person drinks untreated water and gets giardia-maybe she'll understand that. And that you are to use only Corid. There is also a product, same ingredient, called Cocci-Rid. They both are concentrated amprolium. Sulmet doesn't fix all 9 types of cocci and you have no idea which is affecting them; it's a sulfa drug.
You must treat the entire group of chicks. If one has cocci, they all do. Some show worse symptoms than others. Get the liquid Corid, or powdered if they don't have the liquid. If they have neither, Sulmet would have to do, though it's harder on the intestines. If a pal can let you have a 1/4 cup of Corid, that would be swell.
In the meantime, give them probiotics like plain yogurt or even add some nonfat powdered milk to the starter crumble (old farmers cure, though may not actually cure, just soothe the intestines a bit).