Lockhart's use of this made-up spell was apparently well-known, as a question on the 1996Theory of CharmsO.W.L. asked whether Peskipiksi Pesternomi was a genuine charm or not, and required the answerer to come up with a valid incantation that would have the actual desired effect.
It had absolutely no effect whatsoever on the pixiesProfessor Lockhart had released to fly wild throughout the classroom, and indeed had no effect whatsoever.
It is probable that this spell would not be effective in any case, as Professor Lockhart had presumably invented it in that same class, with no forewarning and no indication that it would be successful.
This incantation is most likely derived from English "pesky", meaning "annoying"; "pixie"; "pester", meaning "to annoy"; "no" for negative; and "me" as the first person pronoun.