We are in the process of packing to move and I removed a screw from the wall in the laundry room and water began spraying out from the wall at me. I shut off the water to the whole house now to stop it, but desperately in need of water... what do I do?

You could have possibly screwed into a water line at another time and the screw sealed the hole. Now, removing the screw opened the hole. If water is spraying out the hole where the screw was, it is for sure a hole in the pipe. Cut out a piece of drywall to gain access, solder in a new piece of pipe and repair the wall.