That's what shotgun shells are like in real life. They fire buckshot not solid slugs. Buckshot is basically uniform sized ball bearings packed into a shell with gunpowder behind it.
You need to get the lady to give it to you. Either back the computer or get the passcode from the doctors grave. Login into the terminal and increase her allowance and talk to the old lady again.
Drag the gun from equipped slot to bag space below. This should unequip the weapon and allow for breaking it down. You can also drag a weapon from bag space over the current equipped weapon to swap them out.