If "TOTW" is "Taste of the Wild", our older dog did the same exact thing. It smelled like Godzilla had taken a fresh doodee in our house...on a constant basis. His toots were frequent, and horrid. We switched him to Orijen and everything is fine now...no gas and his doodees hardly smell.
I'm not sure what ingredients were in Taste of the Wild that caused this extremely nasty odor emanating from his booty, but it was horrible.