Well, Fowl Pox presents with little bumps on the comb, wattles, and face. I don't see any of those. If it were Fowl Pox, she would likely get through and not need to be culled.
On the other hand, problems aside from Fowl Pox that are usually diseases that the chicken will carry for life even if she gets past the symptoms. On that count, many choose to cull instead of risking spread of disease.
I don't know what's wrong with her, but i would take a look inside her mouth and see if you see anything unusual or alarming. I would also listen to her breathing and see if you notice any unusual odor coming from her beak. All of these things will help others here do a better job of leading you in the right direction.
I hope she's o.k.