You have a PC, right? Shouldn't you have about nine USB ports?
You can't transfer wirelessly and have them show up in the iPod app, I believe.
Correct,
You can indeed transfer music (using an App called Air sharing - I think it's still free).
You can then connect the PC and your iPhone to the same Wireless network and move any file to the iPhone.
However as Tallest Skil correctly explained, this won't add it to the iPod App.
A (very long winded) solution would be:
1) Transfer files to iPhone using Air Sharing
2) Transfer files to another PC using Air Sharing
3) Plug iPhone into USB and transfer songs