Unusual A/C problem

97 XJ Country 4.0L auto 4x4. I have noticed when I run my A/C on the coldest setting for and extended amount of time (usually more than and hour) no matter what level the blower is set to or which A/C setting (the ones with the little snow flake next to it just to clarify) it will start to blow air however you can here the blowing just the same almost as if it was blocked by something. Now if I turn it off for a while or switch it to heat and take it off A/C and run it for 10 or 15 mins, then this will fix the problem and the air ways will become "unrestricted." After this is done I notice that some water will drip out onto the floor through the driver or passenger lower vents but not both at the same time (I think this is just gravity and which way the Jeep is leaning towards). My guess is this is condensation building up somewhere and then freezing and blocking the air kind of like in a home A/C system but I am not totally sure. Has anyone had this problem or could point in in the right direction on where to start looking and how to get to that area? Replacing the entire system is not an option by the way so anyone with the "hell just replace the whole thing" solution please don't respond with that unless you know there is absolutely no other solution for this problem. My A/C works great other than this problem and it is super cold and I can deal with it if the problem is more trouble or expensive to fix. It is just a little annoying and I would like to fix it if I can.

Look on the passenger side of your firewall, directly over the frame rail, see that little hose sticking out, thats blocked and not allowing it to drain. You need to clear the blockage.

I am assuming you are referring to inside the engine bay? Can you be a little more specific on where exactly the hose is? Sorry just making sure I can find it quickly and I am not out there forever trying to hunt it down. I am in Statesboro in South Georgia and its hot as hell out here so the less time I have to spend the better haha.

When you open the hood and look on the firewall directly above the frame rail you will see a 4" or so rubber hose with a bend in the end, hard to miss, it's the only one there sticking out of the firewall. Some just blow air thru it with a air gun, becareful sticking say a coat hanger in there.