I think 'shit' creek is a more modern version in these less proper times and would not have been part of the popular and polite lexicon spoken when Paddy wrote his songs. Crossness sewage treatment works which serves most of inner London north of the Thames was built on the banks of Barking Creek in the 1860s, so the association would not be older than that, whereas Barking Creek was a port well before that. As to barking mad, that is more likely a reference to mad dogs (of Noel Coward fame) which have rabies - but of course, the Isle of Dogs a mile or so upstream opposite the Millenium Dome at Greenwich had a similar reputation to Barking Creek etc, and to go to the dogs could also mean losing all your money at the greyhound track.