Seems possibly repiratory to me.. coupled with the sneezing.
Hens (even egg laying ones) can crow and it does sound quiet pathetic, similar to what you're hearing at the end.. not *usually* with other males present (which I think I see in the background).
It IS possible though. Some also grow spurs, even without crowing. I do agree crowing would not LIKELY be constant as you describe.
My whole family doesn't always catch the flu when it comes around, since we all have our own individual immune systems. Even flocks that got a Marek's diagnosis won't all succumb to or even ever show symptoms, despite being infected carriers.
I've had my share of broody's and while all vary some in their displays and I value the previous poster's concern, help, and participation and sincerely do not intend to dismiss anyone, I disagree about it being a broody behavior or any part of "normal" hormonal breeding season stuff
according to MY experience. (at least the specific sounds you're concerned about)
I might consider using a flahslight to check the nares for a stuck grass seed, fox tail, dirt, etc.
I can't prove it. Haven't seen any studies, etc. But I do wonder if some chickens might experience allergies.. indicated by no others showing symptoms, so far. Lots of things are already blooming here. Any recent changes from one bedding type to another, or feeds, etc?
Are you in the US? Adding your general location to your profile might help folks make their best suggestion possible at a glance.. regarding what resources (feed, supplements, vetrinary, etc) might be available to you, and any recent avian disease outbreak type information, etc.
Hope you get more ideas and answers and that she continues to thrive!