I know she was choking because I have had a chicken choke before and I know what to look for. The only problem is that whatever was stuck wouldn't go down. The other time this happened it was with my rooster, and whatever was stuck went down after we massaged his throat.
We tried that again with our pullet who was choking today, and we think it went down. We aren't sure though.
The symptoms were, labored breathing, mucus build-up (happens when humans choke too. It's to protect the tissues of the throat when something is stuck), and nothing would go down or come up. My father is also a nurse and he said that she was clearly choking on something.
We gave her some vegetable oil, and some nutri-drench, and we think that helped. Right now she is sleeping, but later we are going to give her some more fluids so she doesn't dehydrate in this summer heat.
I did all kinds of research and didn't find any answers for what to do when a chicken is choking, so we kind of just did whatever we thought might help. She seems better now, so hopefully whatever it was went down.