Since it started last time, it sounds like the pump is OK.
In automotive wiring, 6V when it should be 12V indicates there is a high resistance other than the pump in the circuit. The relay and the pump are in series and you tested in the middle of the two and saw half the voltage, that would mean there is a high resistance upstream of where you are measuring (or in the fusebox). For now, you can use a jumper wire to get where you are going (remove it when you aren't driving) and then pull the fuse box and replace the relay. A high resistance can also be caused by corroded wires or pest damage, though this is less likely.
If the pump were bad and grounding out, it would be blowing the fuse. If the pump were bad and the motor was open electrically, the voltage would be 12V where you measured it. Seeing 6V to me is a red flag that the relay has a burnt connection (high resistance).