OH MY GOSH!! I just figured it out. Good thing, because I was not going to be able to function until I did.
The reason I didn't have a "manage devices" option is because I had not authorized any of my devices (Windows PC, iPod Touch, iPhone) to automatically download anything from my iCloud.
Once I went into my settings and did so, I suddenly had "manage devices," and all three of my devices showed up.
Here's the link to show you how to enable automatic downloads on a Mac, PC, or device (iPhone, iPod Touch).
Hope that helped!
I guess iTunes isn't sexist after all...