What's wrong with my rear differential?

If the noise changes with speed it's likely the pinion gear.

See a mechanic to investigate. Rear differential is likely shot.

That noise is more likely coming from the transmission, not the differential. When a differential starts having problems you usually hear grinding noises which are the gears chewing each other up. They don't usually howel that's usually from the transmission. The bearings and gears inside a differential are so tight together if that rear will drive is probably not going to work if something is that loose in there causing a noise like that. I suggest checking your transmission fluid.

You haven't mentioned whether there's any wheel shake or power loss or if there are shifting issues or shaking in forward or reverse.

As I said when a rear goes its usually a clanking or grinding noise and rears don't usually make that kind of (or any kind of) noise very long before they either quit or seize. Whinning and howeling is typical for a transmission that's on it's way out.

You added oil too late. It's worn out and may need more than just a new pinion bearing.

Lack of maintenance. EPIC FAIL. Cheapest option? Get a replacement from a junkyard.