1993 Pontiac Sunbird Loud and Delayed

I bought my car about 4 months ago with 76,000 miles on it and up until recently it has driven beautifully. Now when the car is first started it will rev up to almost 2500 RPMs. It will eventually settle back down after a couple of minutes and then its business as usual - until I get to the end of my driveway. When I come to a stop and try to accelerate, the car will rev up again and then jerk forward into motion. If I ease my foot down on the accelerator, there's no problem. But the delivery isn't the same. Also, if I come to a quick stop, the RPMs jump down to around 400 and when I try to accelerate it is about 10x worse. Haven't taken it anywhere yet. Wondering if this is something I could fix myself?