Why are only half of my receptacles working after an electrical arc in one of them?
You'll need an electrician to replace/rewire the receptacle that shorted.  The short melted a wire and caused an open circuit to the remaining outlets fed from that box.  If you are lucky, there is enough wire with unburned insulation in the box to re-wire, otherwise, a new run of wire through the walls may be necessary.  Good fuses/breakers should prevent this.  The fuse should blow before the wire melts.  Make sure your fuses are properly sized for the guage wire on that circuit.  Check other receptacles in the home and if any are loose, have them repaired too.  If you have metal boxes, you might consider wrapping the terminals on the receptacles in electrical tape.  This should help avoid this problem in the future.

Pulling a plug out "too fast" wasn't the cause.  Receptacles should be able to handle more abuse than a phone charger!