yep. You got it.
People may refer to themselves "falling apart" if they feel really bad and the whole world seem to unravel. Falling apart at the seams just makes it a bit more poetic, I guess.
Auseinander fallen im Gegensatz zu sich zusammennehmen. Also wörtlich: an den Nähten auseinanderfallen. Zusammenbrechen.
And since the title is Bad Seamstress Blues, the line relates it a bit more to the seamstress
