Engine repeatedly stalled and gave me the codes P0351 and P1390.

So when I was out job-hunting today, my car kept stalling whenever I would brake at a light. When I listened to the engine, it made this constant, low chugging sound, as if only a couple of the cylinders were working and they had to work overtime. Instead of purring, it was more like my engine was coughing. When I was able to drive at speed without braking, the car was fine, but when I slowed to a stop, it would begin jerking about in time with the engine's chugging.

Whenever I would begin accelerating from a stop, my car jerked forward instead of rolling forward smoothly until hitting around 15 miles an hour.

I'd like to know what's wrong with my car, if it's an easy fix, or if it requires a professional's work to handle.