How to put new music on my iPhone?

I have the iPhone 5 with downloaded songs on it (I don't buy songs from the iTunes Store). I have all my music from my previous computer (the music that is currently on my phone) on this laptop (transferred via external hard drive from my old laptop). I recently got this new laptop and installed the the 11.0.0.163 version of iTunes. I'm constantly finding new music I want to add to my phone, so I download it and save it in a different folder on my (new) laptop. How do I, while keeping all data currently on my phone intact, add new music to my phone?

P.S. I feel like I'm leaving out a lot of important back story but my brain is just so fried from trying to figure out what to do so help would be much appreciated
P.P.S I backed up my phone to the new laptop but only my photos and videos were transferred

You are making this sound much more complicated than it really is.

AFTER YOU ADD NEW SONGS TO ITUNES ON YOUR COMPUTER…

Plug in the phone with iTunes opened. When you hit the Sync button, it will only add the new songs.

DO NOT save your music in a different folder on your computer. (I have no idea what you mean by this) Do you mean a different PLAYLIST in iTunes?

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