Humm, thats not that many miles to have this issue. You may want to do an oil change and see if you have an Auburn in your cars axle. Also check out your rear tires diameter, you may have 2 different size tires and that will wear out the differential really fast.
yes auburn was an option if you got stage 3 slp treatment you got an auburn but if not, dont mind what i said earlier, it will be a torsen carrier which is similar to a true trac and if your having problems with it its junk cause they are un repairable or un rebuildable you will be in the same boat as me except i got 120000 before mine broke.
Get yourself a tire stager tape and check the roll out from the center of the rear tires. You don't want to see more than 1/4 of an inch difference left to right. Don't forget to equalize the tire pressure before you start.