That sounds like the jack. You will need to get a replacement jack.
I (and just about everybody else on TB) recommend Switchcraft. You will need to remove the nut on the current jack, without letting the jack itself twist.
Note the location of the wires on the current jack and desolder them. Then solder the wires to the new jack in the same locations.
Put the jack back in place, put the nut on and tighten, keeping the new jack from twisting.
That should take care of it. If you don't solder, you will need to either get a friend to do it that can solder, or go to a luthier. I would think GC could handle this and it should be quick enough that you can wait on it.
Best of luck!
SBMM Ray35, Ibanez ATK300, Fender Modern Playa Jaguar, Squier VM Jazz V, Mesa Walkabout Scout