1989 Eagle Summit Acceleration issue

Just to set the stage the car was my grandmothers and it became mine. It took me a while to get my liscence and my car was fine when I got it. It sat for 2 years not driven. I had the exshaust system replaced entirely and new spark plugs installed. I had the car towed to the garage since it didn't start up to be driven there. Its after the garage that the problem was recognized.

This is the problem in the best way I can describe it. When I push in the gas I do so like you would on any car and it starts out fine. I get up to 20-25 MPh and it stops accelerating so I push the gas in almost petal-to-the-metal and it kicks back and jolts foward accelerating. I havent gone to my mechanic yet but I have been perplexed to what could be causing the situation. I have run that gas tank cleaner through it in case that was the problem but there was no change. Its a great car and has lower miles than alot of people that own one, and my grandmother kept great care of it. Im wondering if it could be a clog in the gas filter but I don't want to do something that could make the problem worst. What do you think it is? And is if the problem is the gas filter is it a do it yourself project. Im 21 and don't know a whole lot about cars.