Not sure if i will be of any help on this. Did you already check the fluid level of the diff and if there are any metal flakes in the fluid My next step would be to open the diff to see if there is any damage or excessive wear on the ring and pinion. Also the bearings can cause a whining noise.
JEEP Grand Cherokee 4.7 Lmtd 2004
HID 8000K in low and fog / Quad Squad member
KYB Gas-a-Just shocks / Pirelli Scorpion ATR 245/65/17 - Transgo reprogramming shiftkit.