Mick: According to Partridge's historical slang to have been to Barking Creek meant to have a bad cough (ca 1820-50). And this is a variation on Barkshire (=Ireland, Barks =the Irish) - A member or candidate for Barkshire - said of one troubled with a cough, vulgarly styled barking.

But in this case "Barking Creek" definitely refers to a location...and one associated with sailors and shellfish, which Barking Creek is. I don't see any point in postulating a convoluted reference to Ireland when the named location fits the subject matter so well.