I created a directory in the root of my project named Sounds
That sounds like the problem right there. You need a folder reference — and instead you created a group.
Here's the correct procedure:
Create a folder somewhere else — say, on the desktop — name Sounds. Drag that folder into your project window's project navigator, and when you do, look carefully at the dialog that appears. You need it to look like this (note the crucial designation as a folder reference):
You'll know you've got it right because the folder icon in the project navigator will be blue:
Confirm that you've done it right by checking that the Sounds folder appears in the Copy Bundle Resource build phase:
Now your strategy will work: Drag files from the Finder into that blue folder in the project navigator, and they will be copied into the real "Sounds" folder. The "Sounds" folder itself will be copied into your app bundle at build time, and you can refer to its contents in code using ordinary FileManager methods.