How to recover the internal storage on my samsung galaxy s3 i9300

the hardware on phones does not support recovery tools for accidental format deletes, if you had a "backup" you could just do a restore to get this data back but if you had no back up then sorry to say but it's gone.

Internal Memory doesn't mount as a drive like external memory does. External memory would allow you to use data recovery tools that scan for deleted files and return them to a usable state. These tools work because most operating systems don't go through and set all of those 1's and 0's to just 0's when you delete a file. Usually the operating system will just delete the reference pointer in the index that says that a file exists with such-and-such name and it's located at this position on the memory location. There are destructive delete tools out there that will overwrite the spot of a deleted file multiple times to discourage recovery in just this manner. The issue is that data recovery tools need an actual mounted drive in order to dig deep and unearth those files