Q: 2003 ford taurus 3.0L V6 check engine light flashing and seems to be coolant issue .

Bottom radiator hose disconnected , didn't immediately notice it and drove for about 2 miles at most , and that's when I noticed check engine light flashing and then the car died as I was coming to a stop . I opened the hood , saw the hose was disconnected, reconnected it and refilled the reservoir tank with 4 2L bottles of water, the tank wouldn't fill completely. Drove for another 2 miles at most , and when I checked that reservoir tank it had like black metal shavings in it , I think but not sure, it's not oil though. It now has a rough idle , temperature never did get over the halfway point between the C and H , still hasn't but there is white smoke coming out the tail pipe but only really when it's idling. There was no check engine light or anything on before this all happened but now the check engine light blinks , then steady on , then blinks again . Do I have a blown head gasket ? Or is the thermostat or maybe water pump ?

My car has 155000 miles.
My car has an automatic transmission.