No the inner shift boot is rubber boot shown in this picture with the 6spd. I know some of the older JK's had popping out issues and stiffer shifts with some of the inner rubber boots.
You can find it under the outer shift boot in in the cabin of the jeep.
However, by the sounds of things you may have some internal issues like the synchros. If you have Powertrain warranty let the dealership look at as it will be covered and should be 100% costs covered by Chrysler.