Welcome to Android Central! Did you load the music on your previous phone yourself, or was it pinned (downloaded) from Google Music? If it was downloaded directly from Google Music, that doesn't go to the external SD card--it resides in the internal storage, and is intended to be temporary anyway. If you did load your own music files onto the phone, are you sure you did it on your external SD card, or is it possible you loaded it onto the phone's Internal Storage (sometimes called the Internal SD)? If you remove your external SD card from your phone and plug it into your computer, can you find any of those music files?
The same general idea goes for your pics. If the pics that are missing were taken by the phone's camera, and if it was saving by default to Internal Storage (I'm not sure the S3 camera even has an option to save photos to the external SD), then those photos are gone, unless you backed them up.