How to restore my Itunes library/save iphone music?

My computer had a virus so saving/copying my old music folder won't work. With Itunes and transferring purchases there are only 275 music files. I have almost 800 on my phone. All I have to work with is a single file where I had exported my library 2 weeks ago. Is there anything I can do to restore the rest of my files? It would be ok if I was able to just add my new music I got today(don't ask not the source of the virus) on my iphone but Itunes says I must erase to do anything with it. 11 free gbs on a 64gb iphone is a lot of erasing and restoring its really just the music I want to save the rest doesn't matter Apps came from the App store.

In fact, once you've put the songs or video on iPod or iPhone, you can get them out of iPod or iPhone and put them on computer.

If the songs are purchased from iTunes. You can easily transfer them to iTunes or computer by clicking "Transfer purchase". If your stuff are downloaded from other website. You can transfer them to computer with iPod transfer. Like this one:
http://ipod-iphone-ipad-computer-transfer.blogspot.ca/2012/08/ipadiphoneipod-transfer-tools.html