How to transfer my songs to itunes?

I have all my music on Amazon MP3 and I just got an iphone so I want to transfer my music to iTunes. But, I can't download iTunes onto my computer because the memory is too small to support it. Can I go to the apple store and transfer use there computers for that use?

1.Turn on your computer. Launch iTunes. You can do this by clicking on the iTunes icon on your desktop.
2.Select the Files tab. Next, select the Add to Library tab.
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3.Locate the file, folder or volume you wish to include and click Open. ITunes will choose which files it can play and add them to your library. You can also drag your selections to the iTunes icon in the Windows Start menu or the Mac OS X's Dock or into iTunes main window.
4.Play a song. To play the song, click on the title of the song and then click Play.

Adding content on your computer to iTunes

iTunes helps you add digital audio and video files on your computer directly to your iTunes library. You can add audio files that are in AAC, MP3, WAV, AIFF, Apple Lossless, or Audible.com (.aa) format. If you have unprotected WMA content, iTunes for Windows can convert these files to one of these formats. You can also add video content in QuickTime or MPEG-4 format to iTunes. To learn how to add these files to iTunes follow the steps below.

Open iTunes
From the File menu, choose one of the following choices:
Mac
Add to Library
Windows
Add File to Library
Add Folder to Library
Navigate to and select the file or folder that you want to add
If iTunes is set to "Copy files to the iTunes Music folder when adding to library," iTunes will copy all content that is added to the iTunes library to the iTunes Music folder. To adjust this setting or change the location of this folder, go to the Advanced tab in iTunes Preferences.

Use a 3rd pary program like sharepod. I doubt apple would help you do anything that does them out of money.

Maybe you should check your computer firstly and find why you can't download iTunes. By the way, maybe you can ask help from Apple Support, maybe they will offer you a solution.

I Do Not think it is a good idea to sync music from the computer in Apple store, because everyone can use these macs, it do worse in maintaining your privacy, you should that iTunes may ask you sign in with your Apple ID. You know what Apple ID means for you, you contacts, your messages, etc.

In my view, if you don't plan to get a new computer now, you can get a some iPhone data transfer software, which is cheap but can help you sync music to iPhone or from iPhone to computer. There are so many kinds of iPhone data transfer software in the market, you can easily get one suits for you.

Here, I offer you a post named how to transfer music from iphone to computer for free, it will show you how to transfer music from iPhone to computer without iTunes.

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Maybe after you read this post, you needn't iTunes any more. Lol