1997 Chevy Cavalier runs fine for about 40-50 miles

1997 Chevy Cavalier Front Wheel Drive Manual 117000 miles

hi, my brother and I bought our cavalier off a lot not to long ago. It drove perfectly all the way home, but the next day we drove it around town for a bit and drove it to bloomington which is about 30 miles away. Randomly in busy traffic it starts "sputtering" I guess and it wouldn't give any thrust when we would pump the gas pedal. After sputtering for a few seconds it dies on us. The weird thing is it starts back up immediately after it dies, but after it dies the first time it starts dying like every mile if we have to stop for stop lights and stop signs. If we get to the highway it's usually fine. It's very upsetting because we just got it, and we really need a reliable car to get us to work and back. We have had our fuel filter changed and we brought it to a shop to check our fuel pump, but they said our fuel pump pressure is fine so they couldn't find the problem. It has died like this more than twice, like I said it'll be fine for a good while, like 30-50 miles. Then it'll start acting up on us. If anyone has any idea what my problem could be will you let me know? I would appreciate it very much.

thanks