The ignition switch recall is surrounding the fact that the key "detent plunger" was not strong enough to hold the key in the on/run position. It would often lose contact and shut the car off or slip to the accessories position. This caused unintended stalling, stopping, or even worse, in an accident it would shut off the computers needed for airbags.
From what I know (and that may not be a lot) your starting issues are not related to the recalled ignition switch. If the car turned on and the tried to turn over, then the switch did it's simple job. The problem is elsewhere.
As far as keeping the car, that is up to you. If it is and has been working fine for awhile and it's paid for, then consider keeping until you feel the repair headaches are not worth it. In the meantime, take all extras off the ignition key ring to keep any of the recall ignition problems to a minimum.