Fuel pump (?) acting up on 2003 Hyundai Elantra

My car has started either "vapor-locking", or the fuel pump is going out. It will begin to sputter, the gas pedal becomes somewhat of a brake pedal. When I push it, I slow down, instead of speeding up. Then it loses power. I have to let it cool down for anywhere from 5 - 20 mins, then it will putt along only to do it again. And so on. This usually happens when the gas is below middle line, and I've been running my a/c. Any ideas what this could be (I'm just guessing with vapor lock and fuel pump), or how to fix it?

Asked by for the 2003 Hyundai Elantra
Has the Check Engine Light /Service Engine Soon light come on? I would first plug in a professional grade scan tool. A good scan tool can look at key engine sensor data without having to do intrusive testing at each sensor resulting in a speedier diagnosis of what is wrong. Fuel trim figures, air flow figures in to the engine, would be important to monitor. There may be computer relearn up dates for your cars computer. Hyundai as a car manufacturer put a lot of free technical information and workshop manuals on line for Hyundai owners. Check out lots of great information.