Car stops. Starts right back up

I have a 97 Olds Intrigue with 123k miles. It has been running fine. No trouble. About 2 weeks ago I ran out of gas for the first time ever. (Well, I was sputtering as I pulled into the gas station). Ever since that night the car will sputter while I am driving. It will jolt a little as if it just received a burst of fuel. Other times it will just stop. Especially when I am slowing down through a turn or coming to a stop. It will start right back up and go again. Sometimes I just have to give it a little gas at the same time.
Could this be something clogging my fuel filter? Or would that be my pump going out?