Clean Up Your Act
Soap operas are called that because soap manufacturers were among the first companies to sponsor the female-targeted serial radio shows which played during the daytime in the 1930’s, and this term eventually got extended to television shows.
By coincidence, the term “squeaky clean” came into use in about the same decades as soap operas, and was intended to describe things so clean they squeak when rubbed. The term later got a boost by Ajax cleaning product advertisements in the 1970’s, though the term now also applies to people without blemished histories or past practices.
Keeping your nose clean doesn’t just mean wiping it thoroughly, but avoiding corruption and shadiness in general. This term seems to be an American variant of the British term to “keep your hands clean,” which arose in the 19th century, and with the same general meaning.