I lost my old computer, how do I get everything from my iPhone onto a friends computer that has their own iTunes on it

I've recently lost my old computer that had my music on it, this was over 3 months ago, I've bought more music through iTunes since then from my iPhone, I'm wanting to backup my iPhone now though, on my friends laptop (windows) they have their own iPhone and iTunes account on their computer, is it possible that I can, sync my iPhone without losing any of my music that is on my iPhone (some of it is previous CDs downloaded to my old computer that is now on my iPhone) and also without adding any of my friends music, or losing any data on my iphone(especially music).