Hesitation under acceleration

[TODD92XLT]

One week ago my fuel pump started the whine and from my experience that means that it's starting to go. I took it to a shop to get done and a new filter. Three days later I noticed hesitation after I started it, put it in gear and drove away. I only does it at the beginning of driveing it. I could be driveing for two hours turn it off and wait ten minute and when I start it up that same thing happens. just today it would start for a second and ten die, then start up fine right after that. It happend twice today. One day last week I noticed the "check engine" light came on for a few minutes. I'm just concerned because none of this has ever happened before. To me, it almost seems like the pump isn't getting enough pressure in the lines at the beginning of driveing. I have no Idea. Thanks.