Rough start and acceleration and coolant loss

I have a used 2012 Prius for 2 years. This is the first time I have had problems with it.
Minor engine shaking presented occasionally at first.
More pronounced after an oil change with coolant loss and white smoke from exhaust after I add more coolant to resovoir. The smaller one has no issues. I used the red zerex coolant by valvoline. I do not know what firestone used in the oil change, just that they would use 0-20 oil.