I agree it may be the fuel pump, but there may be more than one filter to change! A car that age should still have a good pump, but you never know. Clogged fuel injectors can give the same symptoms as well. My first step after double and triple checking for a second filter would be to add a bottle or two of injector cleaner - I like Techron, it works well. See if that helps.
Simple fuel pump check would be to disconnect the fuel line at the engine- while the engine is cold, preferably after it has sat all night. then stuff the end of the hose into a bottle (I use a 2 litre lol) and observe the rate of flow. If it looks normal, you still may have a problem with pressure. Many auto shops can check your fuel pressure for you for not much $$. I d have them do the checking, unless you have a buddy with a fuel pressure gauge.