Jack the car up and turn the prop backwards and forwards to feel for backlash in the crown wheel and pinion.. if you have play then thats prob why its whining as it will be 'out of mesh', either way though its a case of diff out and sent to the transmission place to be fixed or if its a std diff it might be worth looking for a good replacement.

And if you have a spare diff it would be rude not to send it away and have a quiafe ATB fitted to it.. one of the best mods i've ever done to my car. (the track boys will say get a plated but for fast road use i think quaife is better)