iPhone syncing question - I'm a bit confused on a 2-PC setup

I have just gotten an iPhone to replace my BB Curve. I have Music in my home PC iTunes and sync'd it with the iPhone. On my work PC I am syncing my calendar and contacts and such. Is there a way for me to upload the Music from the iPhone to my work PC (one of my authorized computers)? I am only seeing a way to download from iTunes, which would wipe everything out.

Thanks!

If both are PC then I would look for the library file (.itl) on the PC and copy the whole folder to the other computer. Then when you start ITunes hold the shift key which will let you select the library file and select the one which you just moved over and you should have all your music and apps on the other computer. Also, backup your contact list and import the same at the office and you will be all set.

Good luck, hope this helps...