Frank J. Wilstach, comp. A Dictionary of Similes. 1916.

Sick

Sick as a cat with eating rats.
—Anonymous

Sick as a horse.
—J. R. Bartlett’s Dictionary of Americanisms

As sick as a dog.
—Richard Jago

Sick as a Dover packet-boat.
—George Meredith

Sick at heart as the mouse, that the cat lets go a little way, and then darts and replaces.
—Charles Reade

Sick as Lent.
—Algernon Charles Swinburne