How to just upload a few songs to my iphone using itunes?

So, my computer recenty broke and I need to get a new one. I have been using my moms laptop until I can fix mine and I recently downloaded a few songs from itunes that I want to upload to my iphone. However, i don't want to upload my moms music to my iphone. I tried unchecking the little boxes next to my moms songs and clicking 'sync' but that did nothing. I also don't want to upload the songs from my iphone to her itunes library.

When i plug in my iphone to her computer, it comes up as "Sandra's iphone" (my mom's). We both have the 5c but its not her iphone! I don't know how to change that though, if that is the problem. I also think it is uploading the content from my iphone (pictures, apps, etc. To her computer. There's nothing I don't want her to see on my iphone or anything but she doesn't want it all on her computer taking up space.)

Someone who knows that they are talking about, please help. The answer may be really simple, but I'm apparently technologically inept. Haha!

First of all, if you downloaded them on your iTunes account, log out of your moms and use your own.

If you downloaded them to your moms account Try uploading them to a playlist. First you go to the playlists tab on your iTunes Player. You click the little "+" sign at the bottom and create a new playlist. Then go to the library and drag and drop songs over to the side (a bar will automatically pop up when you drag and you playlist will be there.) put your songs in your new playlist and see if that worked.

If not you could go to your account, download the songs from your iTunes. Go to your iTunes and look at the top of the player there's a half shaded box icon. Click on it and go to add files. Browse the folder you downloaded the songs to and pick out the ones you want, put them in your iTunes library (the one without your moms songs) and sync!

If you already purchased song from itunes with your account you can download it from itunes in iphone with Wi-Fi
Or use itools (download it) on laptop
You can change your iphone name from your settings

You can set the iTunes to 'manually manage music and video', then you can drag and drop certain songs from iTunes to your iPhone, this way will not sync the whole iTunes library. Or you can use some third party software like this alternative to iTunes. I always use it to manage my iPhone songs, videos and photos, works fairly well too. It will not delete any files on your iPhone. Hope it helps. Feel free to email me if you need further help.

http://www.reviewstown.com/itunes-alternative.html

Turn off automatic sync (At the top, Press "Edit", "Preferences…", then click the "Devices" tab, and there are two boxes, check the one that says something about automatic syncing). Then, you can right-click any song you want to add to your iPhone, then scroll over "Add to Playlist" then click "Your iPhone" or whatever your iPhones name is. There might be a quicker way to do this, but I don't think there's. It works though.
Then to sync yours uncheck the box again or you can do it before. I don't know if this will add all of her music onto your iPhone, too because I'm not an expert. For this you can call apple perhaps. It is locared on their site: http://www.apple.com/...t/contact/. I don't know their #.
You can rename your iPhone by going to "Settings" > "General" > "About" and finally "Name". Then it should change it on the computer, too. If it doesn't automatically or after a minute, disconnect it and reconnect it and it should change.