Q: Car randomly sways/jerks left or right while driving, like it loses traction for a split second.

Had new tires put on and balanced about 6 months ago. They informed me that my bushings looked like they might be starting to wear, but not enough to warrant any action just yet, and that my motor mounts were starting to wear causing a light creaking noise when accelerating and braking.

Yesterday, all of a sudden, my car will suddenly jerk/sway left or right while driving at speeds of 40+mph like I'm randomly fighting gusts of wind (which it what I thought it was initially as it was extremely windy yesterday, but there's no wind to speak of today and it's still doing it). Easily corrected, but steering briefly feels like it floats or the tires temporarily lose traction, and can be slightly nerve-wracking. I checked tires for any visible damage as well as the pressure, all seem normal. No irregular sounds that I've noticed, and there's no undue vibrations in the steering wheel at any speed. I have no idea what's causing it as I've never experienced the like.

My car has 104000 miles.
My car has an automatic transmission.