96 firebird fuel problems

I need some help here. My 96 Firebird is starting fine, engine runs great until I give it too much gas (like when I try to climb a hill) and then it coughs, sputters, shakes, then the rpms go way down and it dies. Is this a fuel pump or fuel filter or something else? please help! any suggestions welcomed.

Could be a pump, you can put a fuel gauge on it and drive under the condition and see if the pressure is good or bad.

OR

Could be a exhaust restriction, does the check engine light come on?