I think if she's that lethargic that suddenly, with discharge from the nose and eyes, she probably does have something respiratory. It may be viral, and I'm not usually one to throw antibiotics at stuff without knowing that they will help, but she sounds pretty bad. If you isolate her and keep her warm, treat the crop issue, and she doesn't show some improvement in a day or so, I think I would consider giving her some antibiotics. But keep in mind that antibiotics will kill the natural intestinal flora, making her prone to (drumroll, please...) sour crop! But since she seems to already have that and you are going to treat for that with ACV (don't skimp on the ACV, feel free to dribble some directly in her mouth!) you will probably be OK on that end.
But if the rest of the flock has this respiratory whatever-it-is, and you end up treating ALL of them, you will want to watch them ALL carefully for signs of sour crop, and definitely put ACV in their water after their treatment. Someone else posted on BYC that you shouldn't put ACV in the water at the same time as antibiotics, but I'm not sure why, I would think it would also depend on which one you were using.
I'll leave it to more experienced members as far as antibiotic recommendations - the only one I've ever used was injectible penicillin, specific to clostridium infection (gastrointestinal bacterium). So I'm not the expert for respiratory. Anyone have a recommendation?
Personally, after injecting all of my chickens with penicillin, I would choose injectible antibiotics over stuff that goes in the water. Mine didn't want to drink water when they were sick, so they weren't getting their meds anyway!!! (Coccidiosis - they weren't getting the Corid!). We ended up squirting doses down their throats to get them to really start turning around. We lost 9 out of 22 hens. So just a word of warning - medicating their water doesn't necessarily work if they aren't drinking it!
Good luck, and hopefully someone else will recommend a good respiratory antibiotic soon.