This smell is a strong chemical odor that fills the room and gets stronger with time if not actively ventilating. Any indutrial-strength adhesive I've ever encountered off gasses like crazy.

Many of them even contain formaldehyde.

I'm trying to figure out why carpet needed adhesive, all the wall-to-wall I've ever seen is attached just with tack strips along the edges.

Could these crew that installed have used adhesive for hard flooring under the pad? Maybe there is a reaction going on between the pad and adhesive that's creating a gas that's not too good for you.

There should be no reason for new carpet or pad to "gas you out of your house" unless you are possibly allergic to the pad glue that was used.