I have the same problem! I literally have 0.50GB to work with now and I've only had the phone for 4 months. I don't download much apps and even if I delete apps, it'll only be taking Megabytes off my phone.
I added up the space I'm taking up and the total was only 309.04MB! I have no clue how I could've used 15.49GB! I do have a 32GB microSD inserted after I got the storage warning and since the S4 update, I was able to transfer SOME of my internal memory over (like about only 2GBs). I really wanna transfer ALL of it over but I do not know how. Wouldn't it be amazing if we could just have internal memory transfer to SD memory just upon inserting a microSD card? That only sounds logical!
I do have apps like dropbox and pandora but I cannot imagine it taking up the bulk of the 15.5GB that the phone claims I'm using. I do have Clean Master app to occasionally clear of any random junk it can find (usually I clear about 300 MB every time I use the app).
Please help if any of you had any luck with the same problem!! Thanks!!!