How can I check whether my phone is network locked (Samsung GALAXY S3)?
You could try an app to do this, Samsung have removed/changed some of the Dialer codes on the Galaxy range. 

GalaxSim Unlock seems to do what you want, it checks if SIM locked, and offers an in-app purchase to SIM unlock. Please note I have not tested this app. 

You could also pop in a SIM from a friend's device that is on another network and that should tell you pretty quick!