DO THIS AT YOUR OWN RISK, IM NOT RESPONSIBLE FOR DAMAGES OR ISSUES IF YOU TRY THIS METHOD.
ANOTHER FIX that worked for me and many other GS3s from different carriers and about 6 other different android rooted phones: first a quick explanation of why this happens, when rooting and flashing custom roms, it's better to try to start from an almost blank slate, meaning of course factory reset, dalvik cache and all of those steps instructed when flashing a rom.
What to Wipe in TWRP | TeamWin this article explains it better.
Anyways, my process has been this:
1. Installed Root Browser from the Play Store.
2. Installed Clean Master (this app when set up right, will automatically free you up valuable space from junk files, uninstalled apps, temp files, boost your ram and many other neat tricks).
3. IF YOU USE ROM MANAGER, for some reason on the devices with Rom Manager, the app had 1 or 2 backups of the device's previous or stock ROM, taking up to 5 or more GBs of space. These are stored in the device's internal memory, not SD card. Not sure why this happened but get rid of them or move them to the SD card (assuming you have enough space) and BOOM, precious space but there's more

4. The rest of the kidnapped space lies within a protected partition, when flashing a ROM sometimes this partition is left untouched and a different partition is created instead of re-using the old one.... thus giving us the famous LOW STORAGE. The system app that shows storage usage does not reflect partitions or their sizes, reason why when we add up available space, apps, pics, downloads and whatever else is shown in there, IT NEVER MAKES SENSE ("._.).
5. By this time you're already familiar with your device and what you've installed and what you shouldn't have. Open Root Browser, if prompted, download utilities. On the menu bar, go to “Prefs” and make sure that "Show storage bar" is checked which is a great way to see the file size of every single item you select, group or individual.
6. On the root folder, find the folder “Media”, inside of this folder there are many other that contain data from the old partition, this data is the one taking up the remaining space we’ve been looking for. Inside of “Media” there is another folder labeled “Data”, this is the largest folder in the partition.
The trick is to keep whatever you want to salvage, anything else is trash. Take a look at the folders, browse, see if you remember the apps in those folders that are from previous ROMS and delete what you want. Since your current ROM is in another partition, nothing that gets erased from the “Media” folder will cause damage. I erased some “system” apps and folders within “Media” that I thought would mess up my GS3 or the other devices I worked with, the browser, keyboard and other apps had some issues but a quick REBOOT fixes the path that invokes the apps and they work again like brand new.
Run Clean Master to get rid of left over junk and flies, free up some RAM and there you go. Hope it helps. IT WORKED FOR ME ON DIFFERENT TIMES, DIFFERENT DEVICES. All rooted.
This is what Im running...
