'Pa mete bouch ou sou mwen' would this be the same as 'don't meddle in my affairs'?

No.
If you want to use the METE BOUCH to say STOP MEDDLING, then you an say Pa mete bouch ou NAN zafè m.

Mete bouch SOU means to jinx or give bad luck in this original sentence.

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words