Note that sloughing of intestinal lining looks very different from bloody stool. One looks like pink or red-tinged stringy material in otherwise normal stool and solid matter, while the other is bloody red liquid that persists and splats but not a cecal poop which is also smelly.
If you post pictures, we can try to help diagnose whether you are dealing with cocci or something else. A fecal float from a vet is helpful if you think they may have worms or want to test to see what exactly is going on.
While there may be bacteria that cause symptoms similar to cocci, and cocci can damage the intestinal lining which could lead to bacterial infections, there is no such thing as bacterial coccidia. Cocci are protozoa. Therefore Corid is the best choice of treatment for cocci, IF that is in fact what you are dealing with.
Probiotics shouldn't interfere with the Corid, if you're giving liquid probiotics. It wouldn't be recommended if you are dosing with antibiotics though.