Q: engine fires, but rocks violently and will stall after a few minutes of running

I was driving on the highway going about 80 mph (no pedal to the floor) when the engine began decelerating until i could only limp the car about 15 mph. pulled off to the side of the road and fired it back up. engine lit right away, but then would stall within 2 minutes, rocking badly. i had the car checked for engine codes, but nothing came up. It feels like the engine wasn't balancing correctly when it was running. when idling before the incident the rpms weren't always steady, it would fluctuate from a steady 1000rpm to about 700rpm. the sonata had a new timing belt put on less than 30,000 miles ago as well as a new catalytic converter. i replaced one of the coil packs a few months back as well as some of the spark plugs. any idea on how i can figure out what might be the cause?

My car has 138000 miles.
My car has an automatic transmission.