why don't events added to Samsung Galaxy S3 get shown in my Google calendar?
Not sure this if this exactly what you mean but if memory serves from when I ran the stock samsung rom on my SGS2 the Samsung calendar is separate.

When you create events you need to select the calendar you want to create them in.  Obviously, you should pick the google one rather than the 'my calendar' one.

I think you can also set the default calendar after you hit the menu button when you go into your calendar.

If it's strictly a sync problem rather than a problem with adding events you can try clearing the calendar data in your system settings > apps then re-sync your accounts.  Note: take care if you do this, google calendar events are stored in the cloud but if others are stored only locally on your phone you might lose them.

Hope that helps.