In the English language there is a lot of slang, and "Ain't nobody's stoppin' me" is an example of it. Really, what the rapper is trying to say is: "Nobody is stopping me." That would be the correct way to say that.
Tobus, if you're listening to popular music and looking for "proper English," it's a lost cause. Incidentally, the way that rapper speaks is indicative of either a poor education or a particular dialect, depending on how you see it. Incidentally, as a young person myself, I can tell you that most rappers would consider that sentence wrong. Are you sure you didn't mean to write:
Ain't nobody stoppin' me [now].
This is a whole different, unique culture we're talking about and the speech patterns used by people in it is easily worthy of its own CD thread. So careful using phrases like "rapper-man" as it could be seen to be offensive by some forer@s.