@at the op. I used to get them, so I know what it feels like. I have learnt to take control of thing so it is unlikely to get that far nowadays.
Just some reassurance about not breathing. Most likely the reverse is happing, I know it feels like the opposite but medically you are breathing in too much oxygen (hyperventilating). What can happen is you can get lock jaw which may inhibit breathing through the mouth but no the nose. If your jaw is locked and you can't open it, don't be frightened, it is not a bad as it seems, things will be over soon.
Even though some panic attacks can start off with you apparently holding you breath, such as in social anxiety not wanting to be seen to be breathing (yeah I know it sounds crazy now, I also couldn’t be seen to be looking in one place), if you were actually asphyxiating yourself what would happen is you would get high and pass out (which is not the same as overheating and fainting).
The worst panic attacks have happened when I was ill from food poisoning. That is because I vomited my gut out. I lose potassium very quickly, and it got to dangerous level I had to stay in hospital. Anyway if I’m having a panic attack then, it worsens the existing cramping from lack of electrolyte. All my muscles contracted into the tightest hardest masses you can imagine. I literarily was buckled over in agony, my calves were killing me, you can’t open your fist of unbend any of your limbs. But the treatment is simple as the paramedic said very forthright ‘slow down your breathing!’. It may be blunt but it is true.
Regarding the after effects. Unless you are quite unfit, sick, or have a heart problem it is more likely quite good for you, it is a form of exercise. The feeling will pass over time.