I can not tell if the compressor turns on, air blows through the vents when I switch to A/C. But it just stays the same temp as the outside air. I hope this explains it better, I am not very good with mechanical type stuff and am trying to learn.
Keep your jeep running and turn on the AC, then take a listen under the hood and see if you can hear the AC compressor cycling through. If you hear it cycling on and off odds are it is working and just needs a recharge. If that is the case you can go to an auto parts store and for around $30 you can buy a recharge kit and do it yourself. I just went through that issue and now the AC works great.
I wouldn't put money into a recharge kit unless you were certain you didn't have any leaks. Need to figure out if the compressor is cycling or not first. You may want to invest in a Haynes manual for your Jeep.