It looks like everybody in this whole round world Down on me
It seems like everybody in the world is hostile to, negative toward, or critical of me.
The "Down on me" refrain at the beginning can't be understood on its own, until you get to the fuller sentence. This is quite common in songs.
You're correct that it has nothing to do about oral sex, and I suspect that any explanations claiming such are either joking, or wishful thinking. That said, Leonard Cohen's "Chelsea Hotel No.2" with the line "Giving me head, in the unmade bed, while the limousines wait in the street." was about Joplin.