If House did sell stock short due to his prior knowledge of the CEO's business intentions, based on information revealed in his son's medical treatment, House would be guilty of insider trading in violation of the securities laws. This would likely be quickly uncovered due to the publicity about the business.
The episode title "Instant Karma" is a 1970 single by John Lennon. Hugh Laurie later played Lennon on The Late Show With Stephen Colbert.