P.M.
My grandson, a bright and happy 8yo in so many ways, has always showed a leaning toward anxiety (it runs on both sides of the family, so partly, it's just this kid's genetic makeup). In recent months, he almost stopped eating over fear of choking, and he's a pretty skinny guy to start with. He's now been evaluated and is having a treatment plan set up with a team of MD, speech and swallowing therapists, plus a psychologist. Thank God they've got decent insurance, or all of this would be quite impossible.
This may be serious enough that you and your child will need help finding your way through a maze of baffling behaviors and fears back to a healthier baseline. Your daughter is already stuck, and it sounds like you are, too. If you have adequate insurance, I'd start there.
One other thing we have scheduled for my grandboy is a session of EMDR (a simple, non-invasive technique that can significantly defuse emotional problems brought on by a traumatic event, like choking or fear of pain.) It's effective for many soldiers suffering PTSD and is approved and used by many Veterans hospitals. Some insurance plans cover it. It is reported to be very quickly effective for children, and might be a gentle way to help your daughter conquer her fears. You can google this for lots of information.
Wishing your family the best!