Car stalling while driving, will not accelerate

I have had this car for about a year now, and when I was driving it one day, I accelerated hard on the road and the car began to sputter and not accelerate had to pull over and restart the car. Now, after a couple of months, the car begins to stall after a short drive, doing the same thing, sputtering, not being able to accelerate then shuts off when stopped. It will start fine after about 3 minutes but still has the chance to stall.

I believe it to be the fuel pump and filter and plan to have them replaced, but I would like some advice on what it could be. Any thoughts?