2003? V6 Ford Explorer engine surging

This is not my car but my mother's, so I won't be able to tell you much history.

I'm also not 100% sure what year it is, but looking at pictures online I think it's 2003. Currently the car is about 1/2 mile from me, so details will take a while to get.

I'm currently stuck in Rifle, Colorado in 100+ heat, but managed to find a McDonald's with wifi, so here I am! The car is outside of a garage that won't be open until Monday (and about 1/2 mile away in sweltering heat).

I was driving down I70 when the speed limit turned from 60 to 75 and when I stepped on the gas to speed up the engine RPMs started dipping and reving, dipping and reving.

The car wasn't accelerating while reving like this. So I pulled over to the shoulder and checked the gages, which all read normal, no engine lights, etc.

When I tapped the gas again, the RPMs dropped again. Also the oil pressure indicator dropped as well when I did this, so I quickly shut the car off, worried it might have something to do with the oil pressure.

After it cooled down a bit I checked the oil and it was okay. I had the truck towed to a garage but they may not be able to help me until Monday (it's Saturday).

The car does start normally.

So, that's the situation. Off-hand what does this sound like? The mechanic and tow truck driver thought maybe it had something to do with the fuel filter or pump.

What would you fine folks recommend? I have a limited set of tools in the truck.

If the car does drive, would it be bad to keep driving it?

Thanks for any suggestions.