Try skipping the update and start the game once. Go into GT mode and save (it's a button on the left). Than go to Options (also a button on the left of your screen), go all the way down to the last row, select the first button, that's where you can clear your cache.
Hope this helps 👍
Edit: That got mentioned above already, sorry.
You can also try to open your PS3 Internet browser, than go to its options and select 'Clear Cache', 'Clear Cookies' and such. Clearing all that could help too.