Unfortunately, iTunes does not allow music from another source to be pulled directly into their library from a mobile device.  You must download it to a computer first and then upload it into iTunes.  Also, mobile devices are not able to extract zip files without using another application nor are they capable of saving non-Apple files.  iTunes is a very closely held company.  They are not exactly happy with you using another music source so they don’t play well with others.  So no, you do have to use a computer.