There are dozens of "Go From My Window" songs, some associated with the Awake, Arise, Drowsy Sleeper complex of songs, dating back to the 16th century at least.
The Shakespearean song about an love's troubles in the DT may belong with this group or it more likely was composed independently.

Your poem may or may not be related. It is more of a "Get Thee behind me, Satan" refrain. Go from my window or Go from my door are demands common to many unrelated songs.
What is the source for your "parody"? You give no source or information that can help in evaluating it.

Certainly these have no relation to "Norah, Hist the Window," which is a Negro spiritual revision of the biblical story, as stated previously.

You may get more input if you start a new thread headed with 'Quho is at my window? (16 c.). People looking at this thread are mostly interested in Negro spirituals and gospel.