drain the old gear oil and fill it up with new gear oil ASAP. If that doesnt make the sound go away...you probably are going to have to replace the ring/pinion but usually loud howling noises like the one you are describing is just a sign of low fluid so hopefully thats all it is.

it could also be a bearing.

 

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If it's whining really loud, the pinion depth isn't set properly. The longer you drive with it whining like that, the less likely it's going to be that you're able to reuse the gear set once you go in to fix it.

Gear installs are something that should really be left up to someone who knows what they're doing. If it's done properly, you shouldn't hear ANY whining AT ALL from the rear end.