why does my camry stall after driving for 15 minutes acting out of gas when its practically full.

try changing the fuel filter.

your battery sounds like it has a dead cell.see if someone will take it to auto zone they will check it for free in most states.call them first.

If changing your fuel filter doen't solve the problem, then the problem could be your fuel pump especially if it's the original one. Most fuel pumps last 12-15 years before replacing them. Try disconnecting the outlet line from your fuel pump that leads to the fuel injector(s), insert the disconnected line into glass or clear plastic container, have someone turn the ignition key weather the car starts or not you should see a good strong flow of fuel burst out into the container indicating that the fuel pump is working well, if the flow is weak then the pump isn't putting out enough pressure meaning a defected fuel pump.