[CurtEgerer]

I deal with this daily. Are you saying the cooling water from the drill is soaking the wall? If so, it depends on how much water. Bare minimum remediation: holes need to be drilled thru the drywall near the floor and a commercial air mover hooked to them to run air continuously up the wall cavity for a couple of days. It is possible to save everything if the drying starts right away. I've even seen bubbled drywall dry out and you'd never know it was wet. I would call a reputable insurance restoration contractor - they have the right equipment and do this all the time.

If its really wet, its time for new insulation and drywall. The wood framing won't be damaged - just needs to be dried.