Go to your local hardware store and purchase an outlet tester. At least you'll know if the outlet is wired correctly or not. Then you can decide how to proceed. Either way you'll need to work with a good electrician to solve this issue. Most electricians do not ground the outlet, they only use the hot and neutral. If you have romex this could be a bigger problem as the plastic sleeve does not act as a ground back to the panel.
Romex comes with a ground wire inside. Most electricians worthy of the name will always make a ground connection. Where did you get that idea from?