Regarding feed - medicated starter doesn't usually contain any sort of medicine. It usually has a thiamine blocker. And it's such a low dosage, that any that makes it into the eggs is not going to be an issue.
As for something that is safe for all, switch to a grower, flock raiser, or all flock feed. You do not ever actually need to feed layer feed. In fact, for most backyard flock keepers, it's not the best choice. It has barely enough protein for egg production. If you free-range or offer treats regularly, your birds may develop protein deficiencies, leading them to start feather picking or egg eating.
In addition, layer feed contains too much calcium for birds that aren't laying. All that extra calcium, not getting used to produce eggshells, will eventually build up in the kidneys until they fail.