1996 Chevy Beretta Engine stumbles for a few minutes after

Hi, the stumbling happens when I open the throttle. The engine might rev to 2k rpm then drops slightly. If I give it more gas it does not rev higher and feels like its going to die. If I open throttle fast it stumbles to 3-4k rpm and seems fine. So I hold it at 2.5-3k rpm for a few minutes until the hesitation/stumble goes away.

It happens when I leave school during the hottest part of the day. The engine at that point has been off for about 5 hours.

For cold starts I have to pump the gas peddle. It starts fine if the engine is warm.

I have recently changed the air filter, fuel filter, and the spark plugs. I checked the spark plug wires for damage. The car drives like a champ except for the cold starts.