Storage Space, Boot Loop, iOS Failure

Using an iPhone 5s, 16 GB. Only storage I could use however was around 11,6 GB. I assumed this to be the OS, and was kept for safety reasons; which would've been fine, had it not been for the fact that the OS itself was already listed in the list of applications within settings.

Either way, upon reaching this limit, my phone began to act in strange ways - invisible photos that kept on disappearing and restoring themselves, apps instantly shutting down, etc. This was annoying, but did not as of yet prove to be a tremendous nuisance.

It was however when I attempted to plug in my iPhone into my computer and into iTunes that I began to notice bigger issues. The photos were taking longer and longer time to restore, and certain photos wouldn't be restored. During the restoration, I would also frequently be kicked out of the Photos app - only to return to the familiar 0 photos. Upon plugging it into the computer, and attempting to create a backup on iTunes, an unspecified error occurred - which sent my phone into a boot loop (which it is still in).

Neither the method of holding in the volume plus button or the home button have worked. I can manually enter recovery mode without issues, but from here I am limited in my ability to do anything even remotely helpful - iTunes tells me that I must either update, which is impossible because of the space constraints, or that I must restore, which I simply cannot do (due to the fact that persistent unspecified errors have rendered me without a backup of the last four months, including much crucial data).

It seems that the primary issue here is the inability to access or alter the storage of the iPhone without entering it. If one were able to, for example, remove unnecessary applications in order to make the smartphone function once more, that would immediately solve my dilemma; but from my research thus far, that seems to be an impossibility. It is also surprising how there is no option to repair the OS currently on the phone, which would also solve the issue.

If I can either be directed to resources which allow me to edit or potentially extract the data from the iPhone despite it being in a boot loop, or to some applications which would help me repair my OS in order to gain access to the phone, it would be tremendously appreciated. I'm getting increasingly desperate for a solution which isn't just "restore".