What medicine is n that medicated feed? They are not all the same and don't all act the same way. I see you are in the US, thanks for that information. The majority of medicated feed in the US contains Amprolium but still check the label. The majority does not mean all. I'll assume it's Amprolium in what I'm going to say, but if it is something different a lot of this does not apply.
There are several different strains of the protozoa that causes Coccidiosis. Some are stronger than others so are more dangerous. If a chicken is exposed to one of those strains for two to three weeks it can develop an immunity to that specific strain but does not develop immunity to any other strain. Different strains of the bug that causes Cocci might be in your soil or you may have none.
A typical life cycle of that bug is that it lives in a chicken's digestive tract and forms "oocysts". Technically these oocysts are not eggs but think of them that way. These "eggs" pass out the rear end of the chicken and develop or a few days. If they are then eaten they "hatch" inside the chicken's digestive tract. If the numbers of this protozoa in the chicken's guts get out of hand you can have a deadly problem. If the numbers do not get out of hand the chicken develops immunity. So the trick is to introduce any strains you might have but keep the numbers under control.
These "eggs" thrive in warm wet soil that contains chicken poop. They also thrive in warm water that contains chicken poop. It takes a couple of days for these eggs to develop so if you keep the water clean on a daily basis and keep the brooder, coop, and run dry Cocci is generally not a problem. If not, the numbers can get out of hand.
Amprolium is not an antibiotic. It does not affect any other microbe or disease organism other than the bug that causes Cocci. In the dosage in medicated feed it helps reduce how much that bug reproduces. It does not stop all reproduction, it allows some to reproduce so they can develop immunity. But it helps keep the numbers from getting out of hand. If your brooder, coop, or run are wet or they get poopy water they can still get sick from Cocci but the medicated feed can really help.
I do not use medicated feed. I keep my brooder dry and feed the chicks dirt from the run every few days so they can develop the immunity they need. By the time they leave the brooder and hit the ground they have developed immunity.
Feeding medicated feed medicated with Amprolium does not provide immunity. If they have never been introduced to that bug they can't develop immunity to it. A scenario that happens too often is that people feed medicated feed while they are in the brooder and have no contact with that bug. Then, when the chicks leave the brooder and hit the ground for first exposure they stop medicated feed. The chicks have no protection and if the conditions are wet they can get Cocci. Then people complain that the medicated feed did not work. It worked fine, it just wasn't used right.
So what should you do? I don't know, I don't know how dry your brooder is. There is nothing wrong with feeding medicated feed, it will not hurt them. A romp outside on wet soil will not hurt them, it takes more exposure than that to create any issues, but it will expose them if they have not yet been exposed. If the brooder is dry enough and the water is kept clean you should not have any Cocci concerns if you stop it. But you'd probably feel safer if you do get anther bag. Your comfort is an important part of this process too.