Can you die from shortness of breath?

Can happen. Yes depending on how severe and what is causing it. It is important that you seek medical help right away if you experience uncommon shortness of breath.
RU serious ? Of course you can die of shortness of breath: asphyxiation and drowning are every day examples. Pulmonary edema and ARDS are medical examples. If your tissues don't get oxygen, you're a goner.