[GMCDAC]

On the transfer case I would recommend just draining out your old gear lube and then adding the amount that your specs say and do it slow with those upper plugs out. If you have a lot left when you get to the first plug, plug it and keep addin' the gear lube. The tranny is simple enough but It wouldn't hurt to drain it and refill too If you haven't. You couldn't have gotten any water in them while pressure washing. Even if you did a change of lube would be needed.

I don't think those would squeal like you describe though, it kinda sounds like a throwout bearing might be trying to seize up. That could damage the pressure plate and clutch fork quickly. Another possibility is the pilot bearing, which has to spin when the clutch is pushed in and in either case the tranny has to come out. That one can hurt the input shaft on the tranny. Hope it is an easy fix for you.

Later---DAC