I ran a screw through a wire at home, should I worry?
Shut the circuit off. Leave off til fixed.
You took a chunk out of the wire, if not severed the whole wire.  That means it's thinner, or out of contact entirely.
If it's thinner, that means current is squeezing through a narrow part.  This will make the wire hot there.  It could get hot enough to ignite a fire on the wrong side of the walls.
Of if the wire is cut entirely, or passing through the nail, it is bound to start arcing.  Arcing makes a tremendous amount of heat - it will heat up much, much faster than a nicked wire, and could start a fire going in less than a minute.
Drywall is a fire-stop.  That means, fires which start in between the walls are hard to detect. They can become &quot;fully engaged&quot; (turned into a pretty big fire) before you even detect it.
And then what?  It's almost impossible to fight a fire on the wrong side of the drywall, unless you are a pro fireman who hatchets drywall every day.   By the time they arrive, the fire will be so engaged that they'll have to wreck the place to save the structure at all.
Whose fault is this?
Depends on the length of the nail.  If it's 1-1/2&quot; or less, not your fault.  The builder is required to either keep all wires more than that far back from the wall surface, or, put metal guard plates in front of the wires.
Your job is simply don't use overlong fasteners, and if you hit a hard metal thing, stop.