One of the more serious side effects of metronidazole is bloody diarrhea; instructions are to report to doctor immediately if it occurs; this is for people, of course. It is not at all unusual for people to get diarrhea from any antibiotic use. Actually, after lots of antibiotics, it is nearly a certainty, because of what has already been said here, about their killing off the good gut bacteria. I would not presume to advise you to stop the antibiotic, or to give it -- but I would stop it, at least til I could talk to the vet. I would also specifically ask the vet whether she had cocci or worms, if only to see the vet's reaction, but also because you need this information for future reference in her care.
I'd also ask the vet the question about the eggs. Seems strange to me. Could be there is a health code that you can never sell them, but I don't see why you couldn't eat them, after a week or two (if she ever lays any!)
My guess is that she is not broody. Typically, they lay a clutch of eggs to set, then go broody. My guess is she is staying in the nest box because she feels bad, and likes the darkness or softness, or not being bothered, or whatever. Maybe it feels cozy in there to her.
If you bathe her to clean up her butt, which would probably help her feel better, and might have other benefits, you might put a little Vaseline or Neosporin or Prep H or whatever you have on her vent, if only for comfort -- gotta be sore back there....
Yes, live culture yogurt, or probiotics from the feed store, are a great idea, and certainly can't hurt.