Oh no
Yes, feed chicks medicated chick crumbs. Ducklings can't have amprolium, which is the most common coccidiostat in crumbs.
I think coccidia are everywhere, it just depends on what dose the bird gets, what condition they are in, if it's been very wet and warmish (so the cocci breed more), how aggressive a species of cocci it is etc.
I'd get some Baycox from the vet and keep it in for now, but you may find you have no more problems. Hope so