Car surges/chugs while driving and RPM's bounce between 1500-2000

My car has been doing this odd surging/chugging when I am driving. It acts as though I am pumping the gas peddle. It started doing this a few months ago and was very mild and almost unnoticeable. It has since gotten a lot worse to the point the the car really jerks as its surging. The rpm's bounce between 1200-2000 as it is doing the chugging. It does this mostly in the morning when its cold but it does not do it everyday. I have replaced plugs, wires, valve cover gasket, radiator, thermostat, temp control sensor, and ignition control module in the last few months to fix other issues with it. There are no codes coming up at all and my repair guy is not sure if it is the fuel pump or not. I do not want to have to replace the pump if it is just a sensor. Any opinions would be great!
Thank you!