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It sounds like you have a head gasket or piston rings that are going out. White smoke indicate that coolant is being burned. It may not be too bad if you are not getting any smoke during drive. However when you turn the car off and the car is sitting it would accumulate.
You can try adding some bar's head gasket repair and see if it get's better. If not you may need to have the head gasket replaced.
If it's throwing noise from the valve cover it may drip down on spark plugs and get into the chambers. I would go ahead and take car of any external leaks that you see. If you still get white smoke during start up, try adding a head gasket repair additive.