It depends on what 3 prong adapter you bought. Here are two examples of
grounded adapters
http://diy.stackexchange.com/questions/36697/what-is-the-purpose-of-the-grounding-tab-wire-on-a-3-prong-to-2-prong-adapter. Just make sure the that screw that holds the face plate is actually connected to metal structure that holds the outlets. Turn off power to that room and test by plugging in a lamp or something to make sure the power is turned off. Remove the face plate, there should be three wires that are connected to the outlet, red, black and green. IF it has a green wire connected to the outlet you might be ok as long as the wires are connected correctly and the house is actually grounded properly.
You might even want to check all the outlets in your house to see if they are properly connected. Also as kind of a footnote, if you have cable, the cable guy comes out and grounds his stuff which can cause a problem with grounding.
Happy wiring, the Prisoner...