For the love of God, help me transfer ONE song to my iPhone!

I have spent the past three hours trying to transfer a single MP3 (a home recording), which I have added to the iTunes on my iMac (late 2012, 27") (OSX 10.9.5) onto my iPhone 6. At first, after much reading I realized Apple, in all its glory doesn't allow manual file transfer between a Mac and an iPhone. So none of this Airdrop stuff applies.

Once I realized the only way to transfer a song to be played on my iPhone is through iTunes, I began my endeavor. At first, my iPhone wouldn't mount onto my Mac. So I've disconnected my USB 3 hubs, and tried connecting my iPhone directly to a USB port on my iMac. It took me three reboots of my iMac and my iPhone for the two to finally get to talk to each other.

Hoooray! Now that I finally got the two to talk to each other, my iPhone finally showed up in my iTunes.

However, my iPhone was originally synced with my old laptop (which has since died), so Syncing iTunes with this computer presented me with a scary message: I may potentially lose all my music and movies on my iPhone if I sync it with this computer.

Well, I certainly don't want to do that.

I just want to transfer a SINGLE song from my computer onto my phone.

So after more reading, I've discovered that I can click on the three-dots-in-a-circle icon that appears next to my song in my iTunes, then choose "Add To", and then choose my iPhone.

Ok, done. In fact, I've done that about a dozen times now. All to no avail. Nothing really happens when I click those buttons. The song is not present on my iPhone, and I'm ready to call it quits, after some 3+ hours trying to move a SINGLE song onto my phone.

Please, someone tell me, how does a company where things "just work" manage to make something so simple SO difficult?!?!?!?!?

If anyone can offer any advice, I would be grateful beyond belief. Thanks guys! :-)