Is is hot where you are? It's not unusual for hens to pant in hot/humid weather, even if it's not excessively hot. It that's not it, I've found that sometimes when our girls have something stuck in their nose, they will pant (since they can't breathe through their nose) and sneeze (which sounds a LOT like honking/barking). You won't necessarily be able to see anything in their nose, but it's nothing to worry about at all. She'll sneeze out whatever dust got in there and go about her day. Just keep an eye on her for any other symptoms or general lethargy. It may be good to give her some water and keep the other hens from bullying her, if you want to do something, but from your description, it sounds like there should be nothing medical to worry about.
Welcome to BYC!
Welcome to BYC!