A 5C, heh? How is it?
The Folders only show up like that on the device, the DCIM folder which is what you see when the phone is plugged into the PC will have at least 2 folders, one for MOV files and another for PNGs or JPEGs. After there are 500 pictures on the device, a new folder gets created.
Perhaps DISKAID can show you your categorized folders:
Download DiskAid
And they have a new app called "PicsAid" which you should try, link is on the same page. looks like that will do what you want.
The only other place you can access your iPhone photos from will be your "iCloud Photos" folder which is actually your "Photostream" - Windows 8 used to say "Photostream" but now it says "iCloud"
Also, when you create "Folders" in your Photo Library, it doesn't really create Folders in there. Anything you "move" to those folders is still in the original location., the Folders are only links which exist inside the device. At least, this is how it is in iOS 6.1.2, which I have. in iOS 7.x.x, they may indeed allow you to move pics around. But when you plug your Device in to your PC, and open the DCIM folder that is there, what you see is pretty much exactly what is physically on your device.
"PicsAid" may allow you to see your personalisations, I'll download it and see if it works for my iOS.