I believe you are talking about respiratory depression. I used to experience this on codeine. Be careful. That's how most die from opiates.
I even experienced this yesterday on 5 beers and 20mg Valium.
Respiratory depression though is a measure of the respiratory system's current speed of breathing, from a factor of being slower than before, the opposite of stimulation, it is a measure of a relative value, not a specific condition itself. If your breathing slows, that is respiratory depression, if it speeds up, that is stimulation.
It only becomes a problem if it slows down an extreme amount so that oxygen stops going to the brain, the heart stops, and you die, but you would fall asleep before any of that could happen, so if you are conscious, you are not dying of it, and even if you do fall asleep, unless you did a ridiculous amount, odds are you would just nod off and awaken at a later time period, the main risk is if you vomit and thus block the airways causing death from lack of oxygen.
Anyway this is a classic symptom of a panic attack, as the description "feeling they can't breathe enough" suggests an anxiety-based concern, not an actual physical concern.
Getting winded from walking up the stairs would suggest a physical concern.
