I think what you're describing won't meet regulations for a legal shotgun, commonly a barrel length greater than 18 inches and overall length greater than 26 inches. That means you'd be carrying a weapon illegally. That makes it problematic to claim self-defense. And this is before you meet all of the requirements for justifiable lethal force.

Before you even think of carrying a gun for self-defense and assuming you've already gone through all of the usual firearms safety courses it is worthwhile reviewing some wise commentary on the web:

No Nonsense Self-Defense
Masaad Ayoob Lethal Force Institute