Imho, importing them directly from the camera is not the best way (a understatement). Get a card reader, most modern computers have one built in.
As to importing images over and over, if you have deleted them, or moved them to a different folder or location, that would possibly cause this to happen.
After you have imported your photos and backed them up, format your card in the camera before taking more images.
Software like Adobe Lightroom will recognize that you have imported them already, and skip them. Thats assuming that you did not delete someof them from the computer.