the computer is fully updated. I'm going to be using a different computer for the next month, so i tried to connect my iTunes so i could access all my music. when i signed in, it was only showing my purchased music from the cloud. i connected my phone and synced it, but to no avail. i have 140 songs on my other computer, and all of them are on my phone. how do i get the music from my other computer's tines onto this computer? i don't have access to the other one.
You have to copy the music from the other computer (by flash drive or from a backup disk) iPhones and iPods are doesn't allow to transfer music from device to computer
Non-purchased music files [CD rips etc] are on your computer [right now, the wrong computer], which syncs to the phone.
Going back the other way - iPhone to iTunes - requires a 3rd party app, iTunes will not do it. This is ostensibly to at least slow down the illegal sharing of music, if not prevent it entirely.
If you Google, you will find a million less-than-trustworthy sites that claim to be able to do it for free -but I'm not sure that's necessarily the way to go.
I have iExplorer which I've found to be very useful, but that's $40.
LifeHacker did an article recommending Senuti [that's iTunes backwards] which has a current paid version at $20 but free for 1,000 songs & an older completely free version which I haven't tested, but LifeHacker are usually quite diligent in their recommendations, from my experience, so it might be worth a go.