I've had two.
The 'panic' is a reflexive thing. They do numb your throat a bit so that there really isn't much discomfort and no pain, the panic just comes from the body telling the brain that there is a problem.
It is a bit like being under water, your body saying you are running out of air and need to breath, and your brain saying "no way, I'm under water, don't breath".
Do you have difficulty breathing through your nose? If you do, tell them. It is possible to breath around the endoscope through your mouth, but easier through your nose.