No, even though it feels that way when you are in the throngs of a panic attack you will never stop breathing because of the panic attack (presupposing that you don’t have a health condition).
Although we have some control over our breathing, respiration is controlled by a portion of our brain that is essentially self-running. Respiration is a more complex mechanism than simply inhaling and exhaling, which is what we can control, because it includes various interdependent systems that work in a symbiotic fashion and that are under involuntary control.
TIP! did you know that during exhalations, you do not expel all the Co2 from your lungs? That could explain why we are able to hold our breath for a few minutes.