The milky oil and white exhaust are symptoms of coolant getting into the engine, usually through the head gasket.
Sniff the white exhaust to see if is has a sweet glycol smell.
Let the engine idle with the radiator cap off (don't remove it hot.. duh) and watch for bubbles and a build up of pressure or gushing coolant.
A leaking head gasket will allow the cylinder to pump air/fuel into the cooling system on the compression stroke and will take coolant into the cylinder on the intake stroke or after the engine is shut down. The coolant will seep past the rings and then down into the crankcase.
The engine will tolerate a small leak for a while, it may mostly seal once its warm, but ignoring the problem might eventually leave you overheated, stranded and paying a lot more to solve the problem.