1989 Dodge Spirit Gas problems

I have a 1989 Dodge spirit I bought about a yr ago it ran fine for the first 8 months or so now I have a problem

When I first start the car it seems to run fine for the first 20-30 mins then if I press the gas slowly it goes alright but as soon as I push it a little harder even a little bit it feels like im draggin something im not sure why I know im not draggin anything:)
but after about 10-15 mins of this its like my car is about to stall and I can only go about 10-20 km an hour barely I asked the previous owner who is a self taught mechanic and he said it is probobly the fuel filter im not sure but can someone give me some advice on if this sounds like the problem or not thnx