88 cavalier running rough on start up

Hey, I got a 88 cavalier with the 2.0 4 banger and within the first 15 minutes it'll run rough. Kind of stumbles and runs rough while you're driving and will die and when you start it again you'll make if a few feet and it will die. It repeats this for a little while and then finally backfires really loud and then runs like a champ. Any idea what this could be? It was only running on two cylinders about three months ago and I had to replace the ignition control model and it hasn't been driven much since then. I know that the cat is pretty burned out because when it was driven a little while misfiring the cat was glowing after driving it. The tranny also has a leak going on right now.