2001 Neon

I am having problems with my 2001 Dodge Neon. My check engine light comes on when my gas tank is on "E". I thought maybe it was cause I was using cheap gas. I started using Cheveron "Premium" and then the light goes away. I have already had a senor replaced. I jerks a little when I am down the freeway some times. It also sputters and jerks when I back up. Could my air conditioning have something to do with that? I am trying to avoid a large car bill. Can anyone help me?

my first guess would be fuel pump but replace your fuel filter first (since its cheaper) and see what that does if that doesnt work then replace the fuel pump im not saying that this is for sure your problem but most likely its one of the two