1999 Pontiac Grand Am Fuel pump noise and gas starvation

My car has been making an odd low-pitched noise coming from the rear of the car. The noise only last 10-15 mins. And only does it every 4-5 months or so, with nothing in between. It's been doing this for a couple of years now and has never seemed to cause a problem until now. In slow traffic, the car died as I tried to accelerate. It started back up and ran ok for about a mile, then would not accelerate. I feathered the gas which did nothing until I floored it, then it took off and got me home. It died again and this time I noticed that noise. I started it again, it ran about 1 min. Then made the noise, only this time it got higher pitched until it died. Again, and the same thing.
About an hour later I started it back up and it ran fine.
Now I'm worried about it dying in traffic. I've asked a mechanic about it and he said it could be anything and without hearing it, he couldn't diagnose it.
It seems to me that it's the fuel pump. But would it make noise for this long without going out?
I am disabled and on a fixed income so I can't afford a mechanic to look at it.

Please help!