Hhhmmm according to Facebook vet is stumped. The air for me is diffused throughout cells, not extractable in any pocket. Vocal chord disorder causes breathing attacks, severe asthma-allergy-like reactions, and frequent instant pneumonia which goes away quickly but these air pressure attacks are not part of the pneumonia. None of the many specialists I've been sent to know what causes this and say nothing can be done about it. But rest, regular heavy breathing, sips of cool water, and circular firm massage over the heart helps.
Try firm as in inward pressure yet gentle massage, broad circular repetitive motion, over Pooka's heart and chest area, soothing talk to him, for 5 minutes, and see if his temp and heartrate go down.