Simple solution is to replace the outlet with a GFCI which will provide
protection with or without a ground.

older boxes are often too physically small to have a GFCI fit

what you do is buy a book wiring simplified and do some reading.

to check box to see if its grounded try powering a 100 watt lamp
between the metal box and hot side of receptable.

if it powers a lamp it should be a decent ground. generally BX that
spiral would metal cover cable is a good but not perfect ground