How do I know that enamelled wire is actually conducting the current?
The traditional 19th century method is to get a compass.  Away from your apparatus, it will point to magnetic north.  Any magnetic field will deflect the needle.
But your iron core may already be slightly magnetized.  A compass should be sensitive enough to detect a current in a wire, even without (or away from) the iron core.
If your 9V supply is only putting out 100mV, then the chances are you have successfully short circuited it by connecting a bit of copper wire straight across the terminals.  Electromagnets either need a high current at low voltage, or lots of turns of wire to increase the resistance.