2008 saturn outlook XR - 33k only - hesitating upon pick up and during driving

I have a 2008 saturn outlook XR, it was in an accident, but only body damage on left, I got that fixed, have an issue, where when I pick up, it literally drags for about 20secs, then picks up speed, and that happens when driving, stopping and picking up again. If I floor the accelerator it will pick up quick, it feels like it can’t breath, I think there is airflow issue. I have cleaned the plugs, done the injector service, dealership is not able to find the issue. If I’m on cruise it is much smoother, otherwise even when i’m at high speed, it will suddenly choke when speed varies up and down for a few secs. I had the car reprogrammed, have spent almost a thousand doing little things to try and get rid of this issue, I could use your help desperately. Thank you very much.

It could be a plugged fuel filter or a bad fuel pump.

A plugged up catylitic converter can cause this problem, although seems unlikely in a 2008. Have you every got a tank of contaminated gasoline? Have you replaced the air filter? Has the engine timing been verified at spec? Is the vacuum reading ok and all the vacuum controlled devices verified to be not leaking?

Is your check engine light on?
If so, post the codes, please.