How to sync songs from a new iTunes to my iPhone?

So I'm in college and I have a new computer with a new iTunes. I used to use the computer back home to put music onto my iPhone but now I have to use my laptop here at college. Is there a way for me to add music to my iPhone from the new iTunes without losing all the current music I have on my iPhone?

You can purchase iTunes music directly onto your phone. If you have a limited data plan, find a free Wi-Fi.

You can authorise and download your iTunes purchases onto your laptop with your Apple ID and password.

On iTunes go to the top left menu, and click show menu bar. Then go to File > Devices, and click transfer music from device. All your music will go from your device onto your computer

I connect my iPod to 2 computers every day by selecting "manual management for music and video" in iTunes. That way, you can drag and drop music files from your itunes window onto the iPhone tab on sidebar w/o existing files getting erased. This is NOT syncing, where iTunes matches the iPhone

In other words - DO NOT SYNC.

BTW - were these songs bought on iTunes? If not, "Transfer Purchases" won't work. Instead, if those songs are on the old computer, you should have them copied to something like a CDR. You should get into the habit of saving your music to something to protect them from the not-unlikely-enough possibility that your computer will crash about the same time that your iPhone will get lost or damaged.

You can't do it without losing what is on your phone. What happens when you try to move content to your phone is iTunes will make your phone match what is in the iTunes library. Here is an example.

I have 3 Blink-182 songs on my iPhone right now.
I want to sync some music that is on my husband's computer. He does not have the Blink-182 songs in his iTunes.
I try to sync some of his music. It erases the Blink-182 songs.

As a matter of fact, when you plug it in, it will tell you it has been previously synced to another iTunes library and will ask if you want to erase the content to sync it with the other iTunes library. Your only options are to "erase and sync" or "cancel."