The "whizzing" could have been any rotational internal engine part. The key to me is that there were metal particulates in the remaining oil and the engine seized while operating. Typically, if an engine siezes it can be due to a lack of lubricant, major mech breakdown (crank shaft), or a lack of cooling. When you determine what caused you to break down you can tell better what you will need to do to get back on the road (and if it was related to prior week's oil change). Since there was still oil in the engine and it now had metal shavings in it, the oil change is not likely the cause.
If the crank went or some other internal engine part froze or disintegrated (piston, bearing, rod, valve, etc.), I would look at rebuilding (or engine swapping) only if the car was in exceptional condition or you really liked it. Otherwise I would bury it and find another.