Vet scoped down her throat and it was clear, and so was her voice box (which I learned resembles a snail shell). Lungs sound clear, crop is good, no discharge anywhere, and he could extend her neck 60-70% until she started to resist. She's not showing any signs of neurological issues, and can turn her head side to side with no problem. He gave me antibiotic shots to give her twice a day, alternating sides, and an anti-inflammatory shot to give her once a day to cover both infection and physical trauma. She can make a little noise today and extended her neck probably 10-15% while I was cornering her to grab her. I elevated their food so she can eat easily. Whatever it is, I think it's going to clear up in the next few days.
I'm sure the people in he waiting room with their dogs thought I was crazy for paying $76 to fix a duck, but I'd much rather do that than lose one. Thanks for the replies! Hopefully this helps the next person that has a similar issue. Get the duck to the vet!