Transmission Problems after a low battery. Check engine light on code P0720.

Overnight we accidently left something plugged into the car, which in turn drained the battery to very low by morning when we needed it to drive to work, but it still started. Driving to work the battery warning light turned on but nothing more was wrong with anything. Only until 2 days later did the battery light turn off, after a few trips of recharging it. But shortly after it did turn off, maybe 2 minutes, while at a stop light the speedometer went up to 15mph and a little jump forward, while at a complete stop.

So the rest of night the car was driving that way, and even in park the speedometer jumps up to 15mph.

The next morning while driving around we found it difficult to get above 35 mph, without the rpm going over 4000. Now randomly it will have difficulty going over 35 mph with the rpm jumping to 4-5000. Other times it will shift right and we will be going 70 down the highway at a little over 2000. When we stop it jumps a little still and jumps up to 15 mph still.

The check engine light actually turned on that morning also, and the error code was P0720 (Low output speed sensor speed above 15 MPH). We cleared the code, but it turned on a mile later down the road and changed nothing to the way the car drives.

If you have any idea if the transmission has gone bad or if something small is going on, it would be greatly appreciated!