Extreme wheel shake and back left tire

So I got my tires rotated a day ago and I made sure all lugs are tight. I was driving on the highway today and was aware of a bad wheel shake thinking it was my front end which is being rebuilt this week. Turns out someone behind me told me my back left wheel is wobbling any idea what this could be?

 

If lug nuts are torqued properly, and you've confirmed that's true, and all studs and lug nuts are confirmed intact, then the chances are the shop who rotated your tires knocked a wheel weight off and took your wheels out of balance.

Not knowing what wheels you've got on, it's hard to tell you how to confirm. Wheel weights for our area of truck on stock wheels were usually clamped to the outer edge of the rim at time of install. Aftermarket wheels, or those balanced in the last 10-15 years may have wheel weights taped into the inner rim behind the face of the wheel.

I would be confirming the above, then promptly heading back to the shop who did the work to raise hell.

 

I would triple check those lug nuts. This sounds exactly like the not uncommon problem when going to a tire shop of nuts not torqued, or over torque and broken studs. Its happened to me three times over the years after going to a tire shop (which is why now I mount my own tires).

 

If lugs are tight, and wheel is OEM with OEM lugs.

Bent axle or wheel.