ewwww, I'm sure you meant to be helpful, but ewwww
hair of the dog: to be honest, in the situations I have used/encountered this phrase, speaking is usually kept to a minimum. :) Mostly, a beer/drink is pressed into the suffering person's hand and the phrase is spoken. A look of sympathy is always helpful.
"Cure your hangover with the hair of the dog (that bit you)".