I'm not really talking about the trap, I'm saying take it off to be able to get a real look at the pipes. If you're clear below the drain, through the trap, and you can clear any blockage on the drain into the wall and it's all good from the parts you can reach with your hand (glove) or a brush or snake - then you've got some significant blockage well into the pipe and that probably needs a plumber.
EDIT - sounds like you've done that. Welp, that's all i got.