White smoke is water or here the coolant. So Somewhere some how coolant is getting into the combustion chamber of the engine. Since you over heated it and it sounds like more than once. You may have cracked the block or warped the heads. a head gasket will cause white smoke usually not a great deal but constant. A huge flow of coolant may be the entire gasket has failed or no longer seals at all..

#1. When a car overheats ALWAYS add coolant to the radiator to the *top when the engine is stone cold. Fill the plastic coolant recovery bottle 3/4 full. Install a NEW radiator pressure cap from the dealer of the car.

#2. If you had to add coolant to the radiator, the cooling system had a leak. Go to the dealer of the car ASAP and ask for a *cooling system pressure test which will find any external or internal cooling system leaks.

A GM? Good chance the intake manifold gasket is leaking. Not the head gasket, that would cause the anti freeze to blow out the radiator cap. Could be a cracked head though.

Head gasket almost ceratainly blown which is the cause or has occurred because of the overheating

Filling water will not cure the cause, and if it has overheated for too long the head will have warped and the head gasket will have failed. You need a garage to check it out.

Hi that does suggest a blown head gasket.

sounds like a blown head gasket. Check the oil dipstick. if the gasket is blown the oil will look more like a chocolate milkshake than motor oil.

valve cover gasket most likely