By my name, I would say I am more eligible to answer this question.
From the face evidence, i suppose your fd/student does suffer from Panic Disorder (a kind of Mood Disorder). It's caused by the chemical in brain out of proportion etc... that false alarm for panic is triggered, i.e. those symptoms for panic while there is NO real danger.
If your fd/student "associated" these symptoms with certain situations/environments (e.g. flying, people etc...), and s/he tries to avoid those situation/environments, then this will become Phobia (with a purpose to avoid the panic).
There is NO prevention to mood disorder (like immune injection) . But it's highly treatable with medicines (SSRI/SNRI etc....) and Cognitive Behavioural Therapy (CBT).
So far as I know, a quick/immediate way to solve it is breathing in a small bag. Your fd/student's shortness of breath would cause him/her hyperventilation (?, can't remember the term). That is too much oxygen in his/her blood that will lower his consciousness etc.. (cannot remember).
Breathing in a bag/mouth & nose covered with hands can increase the Carbon Dioxide content in the blood and to soothe the him/her.
If you are a pilot/instructor, you should know this. This is IN THE SYLLABUS.