If the Corid treatment is working then I'd think it's cocci. I wouldn't think worms would even have a chance to grow at that age, but i's probably worth a rudimentary check at least. It's pretty easy to do a fecal float and look for visible worms by just putting some fresh poo in a jar half full of water and shaking it, then holding it up to a light.
Even if your vet does not treat birds, the fecal samples they do are the same for basically all animals, and usually only run about $15. That would be the best route IMO.