It could be that the verse parts could be addressing someone who is causing the change inside of the singer, which is described in the chorus.
Also, the song might not have a specific narrative-type interpretation but just be intended to convey a particular feeling.
But is he pregnant with an animal?!? References to 'Your deep growl/Your high whine' and 'Your scrappy fur' and 'sharp teeth' would suggest so. Odd little song.