What happened to all the storage on my iPhone?

I recently took advantage of the iCloud so that I could add all the music on my computer to my phone, so as I attempted to connect all my music, only some it was acute ally downloaded onto my phone, and I was alerted that I hade no more space left. So I ended up purchasing more storage ($20 worth) and I'm still not able take pictures, view Snapchats and download anymore music. In my settings it says that the total storage is 15.0 GB, and I have 14.2 GB available so I don't understand why it's saying "disk full".

You figured out what most don't know. ICloud free account storage is only 5gb max and anything after that you have to buy. Problem is I don't know what you are looking at for the 15gb or 14.2gb readings. That has to be iCloud as I know it's not the phone. Even a brand new 16gb iPhone doesn't have 15gb of space to give you. It's not even 14 out of the box. The 15gb amount has to be your added on iCloud account. On the phone, go into Settings > General > About to see the real total storage amount left for the phone. Best luck.