Actually, "sick as a dog" never included hospitalization when I was growing up. Maybe sick in bed, puking, fever, bad hangover, etc. But hospitalization, being on supplemental oxygen, etc usually ended the cute colloquialisms.
Well, I've been sick as a dog and in the hospital at the same time. It sounds like you grew up in a place with a bunch of humorless sticks in the mud. (Is stick in the mud allowed?)