If you're sure that the problem is with the wall NOT being attached to the floor, then from underneath, can you screw into the bottom plate of the 2nd story wall??? If so, you should be able to get away with 2" or 2-1/2" deck screws.
It could be the sub-floor has loosened itself from the joists. If this is the case, you can shim between the subfloor and the joist, or buy some of those new fangled Squeek Preventers. There's a small plate that screws into the subfloor which is connected to an adjustible 'hook' (of sorts) that clamps onto the bottom of the joist. You then tighten the adjuster and the floor is pulled down on top of the joist!
IF you can't get to the subfloor and joists from the garage below, maybe you can use some 90 degree angle-brackets. Slip one end up under the drywall and drive a screw through the drywall, through the hole in the angle bracket, and into a stud. (Of course, find your studs AND 'mark' a spot on the wall where the location of the hole in the angle bracket is.) Make sure you set the bracket up off the floor about 1/4". Do use a heavy duty bracket if you can. OTHERWISE, you're left with either driving some long screws at an angle into the drywall, through the bottom plate, and into the subfloor.
Maybe there are other ideas. My best to ya and hope this helps.