Q: how can I transfer my itunes music from my phone to a new computer?

You should have all your music in the iTunes library on your old computer - see How to move your iTunes library to a new computer - Apple Support for guidance on how to do this.  If itself, iTunes provides no capability (with the exception of iTunes Store purchases) to transfer media from an iDevice to iTunes - turingtest2's user tip on Recover your iTunes library from your iPod or iOS device describes a number of method / tools that can be used to accomplish this.