What you need to do RIGHT NOW, this moment:
Go out and take the cap off the degas bottle to relieve the pressure in the cooling system. If you don't, you risk hydrolocking the engine.
Leave the cap LOOSE, park the truck and do not start it again until after the following is done.
After that, at an absolute minimum:
Egr cooler replacement or delete the egr cooler
Then, you should flush the cooling system and get rid of the bad coolant (what did you replace the lost coolant with????)
Next, you have to tear back into it and replace the oil cooler
You could do the egr cooler (or the delete) and the oil cooler at the same time, BUT you still would have to flush the cooling system to clean out the gunk that caused the whole issue in the first place. Flushing after installing a new oil cooler can drastically shorten its lifetime, meaning you might only get a month or two out of the new one. This is why you have to address the egr cooler failure first, before anything else.
Once the above is done, the next step is to install a pressure gauge in your cooling system. You want to add a "T" in the small rubber hose that goes to the degas bottle from the intake manifold. You want to watch what that pressure is. If it goes above 16psi (and I think it will), your head gaskets are toast.
Here is what that entails:
Remove the heads
Find a machine shop that is capable of milling these heads flat
Have the heads magnafluxed and hardened seats installed
(basically, you rebuild the head from one end to the other)
If milling is necessary to obtain flat, they can not remove more than 0.008" or the head will have to be replaced.
Here is a link to a thread written by a machinist that works on these heads. Read it:
How to Machine the 6.0
Buy a set of ARP head studs. Do not use the stock head bolts again.
I think you blew the head gaskets. All that white smoke you saw? That was coolant getting burned off. Every time the egr valve opened, the engine drank a big gulp of coolant (creating that smoke). Steam pressure created by this is WAY above what the stock head bolts can withstand, and they stretch. This allows the heads to actually lift a bit and blow the head gaskets. There will be 0 indication of this failure on the outside of the engine. The head gaskets blow between the cylinders, you will never see it until you take a head off.
A $900 tow bill is cheap in comparison......