You do not have to have medicated feed. Most chicks get through fine without it. Mine are not on medicated feed. The medicated feed will not cure cocci but will help reduce the chance of them getting it. And chicks can still get cocci with medicated feed. It depends a lot on the strain of the protazoa that causes it. I they have cocci, you need to treat for it. Do they exhibit the other symptoms of cocci? They are described in my other post. It may not be cocci.
You should not be feeding layer to young chicks. Layer feed is high in calcium and excess calcium can damage an internal organ. I can never remember if it is the kidneys or the liver. They should be on starter or grower until they are of laying age. I do not know if excess calcium could cause bloody poop.