Gs complete exhaust

[Lexy 3]

I had to get the whole exhaust system done 3 months ago ,from catalytic converter to tail pipes.  Beautiful ,quiet, perfect,  then all of a sudden I start to hear a sound I thought was the base from someone's radio in the distance.  It followed me.  Got to parking lot at work and realized it was my car.   Been back toechanic twice .  He says sounds fine.   The base noise is driving me crazy.  $2000.0P JOB.  He says baffle may have broke , it's  internal and can't do anything.  And that happens with after market  mufflers but he doesn't hear anything.  Also he had me look at system when up on the lift,   I noticed what I think is external rust,  after 3 months?.   Any ideas.