Engine racing (Chevy Cavalier '86)

I have a 1986 Chevy Cavalier, and just recently, I accidently left my interior dome light on after coming home from work and it ran the battery down. After putting an overnight charger on it for the night, I got it charged back up, and immediately noticed that upon starting it, the engine was racing. When I drive now, it wants to faster than I want it to down the driveway and I have to apply the brakes harder to stop at stop signs. I put the car in neutral when I'm coming to a stop now in order to save the brakes from wear and tear. When I do this, the car revs up and races the engine, which is just wasting gas.
The idle is very high when I first start the car, and when the car is in motion. But when I come to a stop and driving awhile, the engine slows back down to a normal idle. But when I start driving again, it speeds back up, and the car wants to go faster than I want it to. I actually had this problem once a few years ago too. At that time, I noticed something REALLY strange! If I stopped on a hill with the car shifted in neutral, the car's idle would eventually slow down to normal. Then if I took my foot off the brake and allowed the car to start coasting forward, the idle would suddenly become fast again. The same thing happened if I had the car shifted to "drive" when I did this, causing the car to lurch forward and start accelerating.

After several months of putting up with this problem, the problem went away all by itself. Now it seems to have returned. I hope to discover what the problem is caused by so maybe I can make it go away sooner.