It's possible it could be Coccidiosis, treating with Corid won't hurt her.
As for antibiotics, do your research and come to a decision whether they might benefit her or not. Having a purplish colored abdomen is not normal, so something is going on there.
Are you keeping other chicks with this one?
If it were me, I would consider housing the CLB separately just in case it does have infection that could be passed through the poop.
I'm sorry that she's not thriving, if you happen to lose her, then getting a necropsy through your state lab...
OK, so she's a CLB, so her skin color should be a shade of yellow - is it just abdomen that is a purplish color?
I'm not a vet nor expert, but I would give a good guess that she's got an infection.
@casportpony and @Eggcessive may want to chime in as well.
An antibiotic may help her-hard to...
What do you feed?
Any way you can take a poop sample to your vet for testing?
You mention drinking lots of water - is her crop empty first thing in the morning before eating/drinking?
Green poop can be from a number of things from infection to not eating well. The mention of the abdomen being...