First check the rear drive shaft center bearing, these can wear and make a fast noise. There is also a possibility that you have a bad wheel bearing, this makes a somewhat slower noise.

If the noise changes when you are on and off the throttle, this generally indicates the ring and pinion mesh is not correct. Severely worn bearings or worn out gears will cause this.

For a used diff check car-part.com , this is a nation wide salvage yard search where you then call the yard directly. Don't even bother with the e mail contact in any yard, few read their e mail.