If yours free-range and are in contact with the ground they have been exposed to whatever strains of coccidiosis are in your ground, whether it is wet or dry. If yours have been exposed regularly to the ground for three weeks, they should have developed immunity to that (or those) strains.
Coccidiosis is more likely in warm damp climates like the Gulf Coast or Deep South where it is warm and wet, but it can be anywhere, especially around wet spots around waterers or things like that. Warm brooders can be a dangerous spot but if they are reasonably dry probably not that big a risk. It’s just not as likely to be a problem in a cooler or drier climate. I don’t know where you are. You may be in an area that is not high risk but you still need to know the symptoms and be on the lookout for them.
The dosage of Amprolium in the medicated feed does not kill all the bugs that cause coccidiosis. It limits the number of bugs but still allows enough to live and reproduce so the chick can develop the immunity it needs. Amprolium is not an antibiotic. It will not kill the probiotics the chick may have in its system. It will not harm the chick in any way. There is nothing wrong with feeding a chick medicated feed, but if the chick has not been exposed to the microbes that cause coccidiosis, it does no good either.
The microbe that causes coccidiosis thrives in wet soil, especially wet manure. A little damp is not bad but a wet brooder, coop, or run can be a source of danger, especially if they have not developed immunity and it is a little warm. When the weather sets in wet there may not be much you can do with your run. That’s a time to watch them closely.
A common occurrence on this forum is where someone feeds medicated feed to chicks in the brooder that have never been exposed to the coccidiosis bugs, then stops the medicated feed just when they go outside and come into contact with the bugs for the first time. Especially if the weather is wet, those chicks can get real sick. If you use medicated feed, it needs to be used for about three weeks when they first come in contact with that coccidiosis bug to help protect them. They can still get sick on medicated feed. There are some strains of coccidiosis that are stronger than others or if the brooder or run is wet, they are still at risk. The medicated feed makes it a lot less likely that coccidiosis will be a problem, but it is not a guarantee.
I don’t use medicated feed. The way I handle it is to take dirt from the run and feed it to them in the brooder starting around day 2 or 3. I don’t feed them a lot of dirt but feed them some every two or three days to keep a steady supply of those bugs so they can develop immunity. This also gives them grit and passes on any probiotics the adult birds have in their systems. My brooder is too dry to rely on them passing on a steady supply of microbes to each other through them eating each other’s damp poop. Chickens eating each other’s poop is how they develop flock immunities and share probiotics, by the way. It’s a good thing, not a horrible yucky thing.
I don’t know if that chicken has developed immunity or not but from what you describe I don’t think it is in mortal danger. You should always keep an eye on them but I really would not worry.
