White smoke is not oil.

Oil burns blue and will smell like burning oil.

Coolant burns white. Blown headgasket?

 

How do you blow a headgasket changing the oil? the smoking is all gone now, even on a cold start.

 

I'm not saying you did.

I'm saying that white smoke is not oil. So thus it can't have anything to do with your oil change.

 

The problem with "color of smoke" is the bluish smoke from oil is often mistaken for white (which is usually very white)....unless you have seen it it is easy to mistake. I believe the OP actually has the bluish smoke FWIW