White smoke from under the hood

Unfortunately, this is likely to be a very expensive repair. If the engine was low enough on oil to have caused severe overheating (probably), it will likely have damaged the bearings, pistons/rings, crankshaft, cylinder walls, and other internal parts of the engine. The white smoke is a visual indication of warped/cracked head(s) rather than just a damaged head gasket. In any case, the damage won't be truly apparent until the engine is torn down. You must be prepared for a whopping bill if you elect to have this engine repaired correctly. It would probably be better to find a used engine in a wrecking yard and have it installed--or to find another car that could give you good service. Good luck!

Crack head no you can't see, but if your car is running with a bad cylinder miss ( rought ) or your having to keep adding coolant, then it has a blown head gasket or a crack cylinder head, to check it for an oil leak from a gasket it's best to take it to a repair shop, where they can put some dye in the oil to find the oil leak.

There could be several causes and it would be quick for an auto tech too figure out but i cant explain it all here you ned too have it looked at by a proffesional

I would almost think that it's steam.
You might have a pinhole in a rad or heater hose.
It could also be a head gasket, or intake manifold gasket.

If you have a boyfriend that doesnt like dirty hands and cannot check the oil or change a household plug or set the washing machine then ditch him and find a more pratical one or you will be working for the rest of your life to pay all the tradesman ,i will no doubt get another warning from admin?? ,right problem with car now white smoke is usually a signal that you have a water leak and its dripping on the exhaust which could be a perished or split water hose or it could be oil but without seeing its very difficult to advise ,if its very low on oil you will hear a pronounced knock from the big ends or the cams these will suffer first but providing you had more two pints of oil in i doubt this but the low oil can cause the engine to run hot as the oil also acts as a coolant to a degree .now best advice i offer without lifting the bonnet myself is to have a look for anything obvious yourself like the coolant level and the oil level then let engine idle for a short while and keep looking for any leaks ,coolant will smell sweet and sickly and oil will smell like oil on a fire burning ,if you cannot see anything obvious then it may be ok and might have just run hot and some of the grime on the engine was smoking but if you see any leak then consult a local mechanic .