Re: new shotgun vs another barrel
they're not very expensive (the whole gun) but barrels are still cheaper. No need for a new gun really, that receiver will hold up to many times more rounds than you will ever likely put through it.
I would try and find a used one, many don't get used very much and can be had much better than new ones.
So +1 for just a new barrel
"Loud noises don't end gunfights.... well placed shots do."