Sounds a bit like reactions I had to rotting building materials in our house. In our case it was the roofing stuff, that particle board stuff. It stunk realllllll bad and burned my eyes and my throat real bad too.
This was NOT a formaldehyde thing, and did not smell anything like the "F" I smell in units in the heat that have been closed up for hours/days, etc.
They are TWO different smells, both obnoxious and both will burn tender areas, like eyes, nose, back of throat, etc.
There may or may not be mold involved if it is rotting building materials.
I would start looking for a leak?? And rotten wood. It will not smell as bad when it dries out for a LONG LONG time, but, get it wet again, and whewie. BAD!
Just something else to consider.
I like the idea of tracing the VIN number.