You should park your truck on an incline, nose down. Pull your egr valve and leave the hole open overnight. In the morning, check the bottom of the hole for the presence of moisture.
If you find that, you have a failed EGR cooler and a plugged oil cooler.
Don't just ignore this. The repair as it is will be around $1300, ignore it and this repair can balloon to the 5-6000 range.
Typical home tools are not enough to tackle the egr/oil cooler replacement. It requires a very good selection of ASE and metric sockets ratchets and ratchet wrenches. You will also need an in/lb torque wrench as well as a ft/lb torque wrench. This will take you about 10-15 hours if you are mechanically inclined and have the tools.
If you see the wetness in the egr valve hole, what is happening to your truck is that it is ingesting coolant from a failed EGR cooler. Should the engine ingest enough coolant, the resulting steam pressure will lift your heads and pop your head gaskets. The coolant is also flowing the opposite direction when the truck is off. The coolant is flowing out of the failed EGR cooler, and down into the exhaust manifold on the passenger side of the truck. Should enough coolant leak out and find an exhaust valve open, the result could be a hydrolocked engine.
What happened the last two days is that there is coolant in the exhaust manifold in the morning. You start the truck and force that coolant to flow through your turbo. The white smoke you see is steam from burning the coolant. Sending the coolant through your turbo can also result in an overboost condition, and an engine weakened by the previous events leading up to this can also result in popped head gaskets.
Check the first link in my signature line. It will give you tons of info that you as a 6.0 owner need to know.
The second link is all about getting the junk out of your cooling system, previous to this repair if possible.
The third link will show you "what you are up against" if you just want to check out what is involved in this repair.
Do the test of parking on the incline and let us know what you find.