The initial incident occurred while pulling out onto a road from a complete stop and had to almost immediately come to an abrupt stop. The check engine light came on and I could not accelerate normally. I had to push the gas much farther to get moving. I drove down the street and parked for 10 minutes. When I started the car the CE light was off and I could accelerate normally. In under a minute the light was back on and there was lag in accelerating again. At the next stop light I turned the car off and immediately back on. The check engine light stayed on but the acceleration was fine. The car seemed to be shifting increasingly "hard" also.
The problem didn't appear again for about a week. A week or so ago while driving up a large and steep hill the check engine light came back on and the acceleration issue was back. The car was parked at home and not driven for a few days. I drove across town last Thursday without problems but once there the check engine light came back on and the acceleration issue was back. It was shifting quite hard now. I also noticed that it seemed to be stuck in 2nd or 3rd gear, perhaps explaining why it wasn't accelerating from stop normally. I turned the car off and it went back to accelerating/shifting, with the check engine still on. On the highway at about 60mph the car seemed to chug heavy twice, as if the car was going to shift/slip? down a gear. Once home going from neutral to reverse caused a very heavy shift/clunk. I've not driven it since.
Other points that might be important: I drive infrequently. I'm not the best at maintaining the car regularly, and for the past 6 months I've sometimes used down-shifting (going from drive to 3rd to 2nd to 1st to neutral) to help slow me down to prevent wear on the brakes but my car is an automatic.