It's likely not a heat sheild issue. You need to check the exhasut pipes where they connect to the engine block.

It is highly likely they have a crack in them.

The sound should be like a buzzing sound. It is the pressure of the exhaust fumes rattling the pipes.

delaer will tell you "it's the heat cheilds" which is a crock. In my 92 Civic the heat sheild rattled when warmed. The sound you are hearing is a buzzing. Different prob then heat sheilds.

Sorry to bear the bad news. It is also a little costly to have this fixed.