correct wire size??

AVG 6 wire can't support 100amps, only about half of that, so if that is what you really need, yes you need to upgrade. Another option would be to see if you really need that much and downsize your box. I don't know how much your AC pulls, but a water heater is typically around 16 and the frig is 5 (typical power usage for the home). The lights and fan are maybe two. You need some overhead for power tools, so it's going to be close.

As for pulling the wire, I would tape them to one of the existing wires and use that wire to pull the new wire through.