Music Syncing Problems

To make it short:

• A sibling bought music on my iPod touch 5th generation without my knowing
• It wasn't much, didn't care for a while, just deleted the music eventually
• No problems until the software update

After the update, the music has appeared: On my computer when I look at my ipod's music, every time I connect to the internet with the cloud icon, in my itunes purchased area, and on my computer after I've deleted it about 4 times. I decided to purge the ipod and deleted all the music after saving it all to a computer and deleting the specific songs. I literally was unable to swipe them to delete on my ipod.

Now, I have an ipod with no music because can't simply "drag it to the ipod on the side", and to make it worse itunes insists my phone is full of music, including every song I deleted but no new music I bought. I don't know what iTunes I'm running because it's not under "get information" and I refuse to waste another hour searching for where they squirreled it away in what I'm sure was a very clever place.

Am I missing something? Is there an obvious way to simple right click and transfer music? Is anyone else unable to add music? Am I actually doomed to have terrible music follow my computer and iPod until I make the inevitable switch to an android?

Quite frankly this is the last straw and if I can't even listen to my music I'm staying clear of Apple products forever.