Music from iTunes onto my iPhone 5c?

So I'm 16 and have an iPhone 5c and I've had it for about a month. I have stuff on it already that I don't want to lose like music, contacts, apps, and pictures. Before I had my own apple id (years ago), I used my dad's but then I got mine. For some reason I continued to put whatever money I got for iTunes on his account haha. But most of that music was for my iPod. Then when I got my phone, if I logged out of my iTunes id (on my phone) and logged into my dad's, I could download only some music that was on our computer but not all. I don't know why. The rest of the music I want on there I have on my computer's iTunes. Can anybody tell me why it's doing this or how I could get the rest of the music on my phone? Do I have to plug it in and sync everything to my phone and make a new folder on iTunes and then drag all the music into that folder for my phone? And if I do have to plug it in, will I lose everything? Because I really don't want to. Is there a way to do it without plugging it in? Also I bought a song off of my iPhone and it's on my iPhone but not on my computer so if I plug it in will I lose that song and that money too? Sorry, it's so much haha! But thanks in advance! It means a lot!

Any songs or media you purchase with an Apple ID will remain on that account. Once you log in, you have access to download it if you don't have it. If the music was on your computer and want to sync it to your phone, you can plug it in and sync it onto your iPhone. However if you have songs from another computer sync to your phone and want to add new songs you must have the previous songs you sync on your computer along with the new songs you want to put in, otherwise it will erase everything and put in what you have that you want to sync. ITunes can be a bit complicated when syncing files and music. You may try an alternative software like "iTools" that allows you to import and export music from your iPhone to your computer and vice versa and many other features. However solve what you need to do first and backing up what is on your phone and computer is essential!