"cat," 1520s, but probably much older than the record, perhaps imitative of the hissing sound commonly used to get a cat's attention or the noise made by the cat in hissing. The same or similar sound is a conventional name for a cat in Germanic languages and as far off as Afghanistan; it is the root of the principal word for "cat" in Rumanian (pisica) and secondary words in Lithuanian (puž, word used for calling a cat), Low German (puus), Swedish dialect katte-pus, Irish puisin "a kitten," etc.
Applied to a girl or woman from c. 1600, originally in a negative sense, implying unpleasant cat-like qualities, but by mid-19c. in affectionate use.
The little puss seems already to have airs enough to make a husband as miserable as it's a law of nature for a quiet man to be when he marries a beauty. ["George Eliot," "Adam Bede," 1859]
Children's game puss-in-the-corner is attested by that name by 17-9.
"the face" (but sometimes, especially in pugilism slang, "the mouth"), especially when sour-looking or ugly, 1890, slang, from Irish pus "lip, mouth."