Another piece of important information is whether or not you still have an intact EGR system.
Your original EGR cooler is a weak design and if the oil cooler is plugging, it can be starving the EGR cooler coolant flow and that might rupture also. Ruptured EGR coolers can possibly hydrolock the engine and that can cause more damage.
You can try backflushing a plugged oil cooler, but many/most end up needing to be replaced. If you replace it, then replace the OEM EGR cooler with one from BulletProofDiesel (if you plan on keeping the EGR system).
There are other things for a new owner to know, just let us know what the code is.
Also - every 6.0L owner should have a scan device to read engine parameters. Forscan and Torque Pro are two good phone apps, and only $5 or so. Then you need to buy an ELM 327 device to plug into the OBDII port. Getting the Bluetooth or WiFi version will depend on your phone and the app you choose. With the scan tool, you can troubleshoot things like this without taking it in.