If plugging the phone into a computer doesn't show you the pictures, and they're on internal memory, not the external SD card, there's no way to retrieve them. Which is why there's an old computer saying that goes, "Any data not backed up to at least 2 independent destinations is data you don't need." (Cloud accounts count as destinations today.)
ALWAYS back up anything you don't want to lose if the phone disappears. Backing up to your computer and 2 cloud accounts (about 10GB is free today on most cloud accounts) means that unless the world suffers a geophysical catastrophe, or civilization comes to an end, you still have access to your data - somehow. I realize this advice is a little late for your situation, but it'll keep you from running into the same problem again.
(If you can find a shop that "plays with" cellphones, and has files to do a non-destructive flash of your phone, they may be able to flash the phone without losing the data, but that's way outside normal repair channels. Most repair shops know how to follow the repair instructions - a shop with a tech who contributes to the XDA Developers forum may know how to save your data. I know it can be done with the AT&T Note 3 [I have the files] so it can probably be done with the S3, but someone had to figure out how to do it and created the files for your model of S3.)