How to put my music back on iTunes?

I had to swap my iPhone for a new one because my last one broke, and my computer crashed so I lost everything on it. Is there a way I can get my music back on my computer? I already authorized this computer on my iTunes account.

So you means you want to transfer your music from one iphone to another new iphone? Yes, see below:

After connecting your new iPhone to the computer and its icon appears in iTunes, you can choose Transfer Purchases from the old iPhone from the File menu.

Or you can right-click (Windows or Mac) or Control-click (Mac only) your iPhone in the iTunes Source list, then choose Transfer Purchases from the shortcut menu that appears.

Please note that this feature only works for items that were purchased on the iTunes Store. Any items imported from audio CDs or acquired from other sources will not copy from your iPod or iPhone to the iTunes library.

Hope that helps you out.