1997 Chevy Cavalier Acceleration Problems

Hello, I am having some issues with my car. I have gotten a tune up and replaced all the necessary parts. I have gotten and oil change, oil filter, fuel filter, air filter, new spark plugs and wires. The problem is this. I will be traveling at any speed but normally going about 20-25 mph and when I try to accelerate above say 20 the car holds back but yet the motor doesn't change in sound or increase in speed. Then all of a sudden the car will jump about 5 or more mph. And make a loud thumping kind of noise. I have gotten advice to up the gas to a higher octane. It fixed if for about 2 weeks then I started again. I was told to get a tune up and a fuel filter could really help. I have done that and it helped but a week later it started up again. Then told to go to another octane higher and try a fuel system cleaner. Worked for about a week. Then it started back up again. The only thing I know is left is the fuel pump or the distributor cap. Can you help diagnose this problem? Thank you.