1996 Chevy Corsica car not accelerating while not warmed up

When I start my car for the first time of the day or after a really long time if I dont give it like 15 20 minutes to warm all the way when im driving itll just nosedive at around 10 20 and 30 miles per hour and after the dive if I pump the gas itll get threw it and sometimes gives a litle jump foward, I had the car for about 6 months nd have only had this problem for about 1 month, I dont think its the transmission because once the car is fully warmed up it drives like a dream. I have not changed the filters in the car and as far as I no there the same ones since the care was purchased 13 years ago, could this be my problem or is it something more serious