1995 Buick Park Avenue Fuel problem every 10 miles

Car runs fine for 7-13 miles, then the check engine light comes on and the engine starts to hesitate. It's almost like the car's not getting enough gas or the gas/oxygen ratio is out of whack. Could also be transmission, as maintaining speed causes the RPMs to go sky high. Best fix is to pull over immediately and turn the car completely off. Let it sit for anywhere from a minute to 15 minutes, then you can restart and continue driving. Problem will repeat itself after another 7-13 miles.

If you don't pull over, the car will continue to run for another few miles but the problem will get worse and worse until eventually the engine dies. If you let it get to that point, it takes a lot longer of a wait time before it will start again.

Problem has persisted without getting better or worse for about a month. We still use it for short trips and will shortly be getting the money to fix it IF we can figure out what the problem is!

Your help would be greatly appreciated, as we are a one-income family on a tight budget. Thank you in advance!