Why does my iPhone 5s never have storage?

My iPhone 5s has, within the past year, been causing me serious issues in terms of storage. It currently still has iOS 7, which I recently tried to update because I figured maybe that was contributing, but the update would never complete. Anyway, it is constantly giving me storage messages, saying it has no room to back up, etc, etc. I've tried to clear space. I only have three apps on my phone at this point (deletable ones, I mean--there are of course the apps that you can't delete). I have only twelve pictures, only ten songs, etc. I've removed all my pictures in the past and nothing has changed. IIm losing my mind with this because it is making it so that I can't take photos, can't download apps, can't send photos etc. I've tried googling it, but can't find anything that helps. If no one on here can help, my next stop is probably the apple store. Does any one know how to fix this?

God sake, just get a [f]ucking Android… S6/Note5/LG4/Z5 etc. Etc.

Clear some space.

Check it and see

Try resetting your phone. It won't erase anything except the garbage files that seem to be clogging your phone. Hold down the on/off button and the Home button at the same time for about 6 seconds. It'll then go through a reset cycle that will take a minute.

Also make sure you don't have a lot of saved text messages, reminders, notifications, calendar entries, documents, and emails.

If you go into settings and then about you can see how much space everything is taking up. Delete some videos that you don't need and some apps that you don't use. Some apps take up a lot of space. You can upload photos and videos that you need to free cloud storage. I recommend google drive as you get 15GB for free.

Worst case scenario:
Backup your iPhone to iCloud and then go into settings and erase all content and settings. You can restore the phone from the iCloud backup. I used to have to do this every 6 months or so after deleting a lot of files.