Goober - sorry to hear what your DD is going through.
I know you have been to see the GP and waiting for test results to exclude physical causes of your DD symptoms.
However, it seems to me that Cognitive Behavioural Therapy (CBT) might be ideal for your daughter.
Here is a link:
CBT
Try to resist your daughter being given something like Prozac or other similar drug to relieve her anxiety. It is not a long term solution.
I had several sessions of CBT - although it turned out I really did have a physical problem that could not be cured by CBT.
However, I found the CBT training I had was very useful in dealing with stress.
Young teenage girls like your DD are under a great deal of stress from the modern world. Moving to a new school, physical changes to her body and dealing with relationships as well as perhaps academic pressures could all perhaps be 'triggers' but CBT would aim to help her with the 'fear of choking' itself rather than dignose and deal the trigger cause.
Have a look at the link above and Google CBT before you go and see the GP and talk to him/her about it. Sadly GPs tend to reach for Prozac as a quick and easy cure but many GPs do not know about CBT.
It would probably require a refferal to a psychiatrist and then on to a psychologist to administer the CBT training.
All the best - this is a horrible thing to happen to your DD and you.