Honestly, she sounds like the chick I had with cocci. The other brooder mates were all running about and she just sat there in a heap. The feed store was going to cull her but instead gave her to me. IDK if your chick has cocci but I do know there doesn't always need to be blood present in the stool for it to be there. You could
try giving her Corid as it can't/won't hurt her. You should start seeing improvement by day two. Also, I am far from an expert
. I just try to share my personal experience like others here have done for me. Good luck and please keep us posted.
Chick before treatment...
Chick after treatment