sounds like your pinion gear and nut are loose.
pull driveshaft and see if the nut is loose.
its cheaper to buy another rearend.
+1 on checking the pinion nut, they are notorious for loosening, you can try tightening it but keep in mind that anything you chipped off the ring & pinion are now in your rear axle. The spider gears are usually pretty good at pulverizing loose pieces which will intern get into any bearings/seals. Unless you catch a catastrophic failure immediately, or you have a rare/original axle you want to keep for some reason, I am a big fan of scrapping a metal contaminated unit.
Which brings me to Idiot's second very valid point: there's a ton of good used rearends out there that will fit your rig for cheap. Also bear in mind that if you choose to repair your ring & pinion, there's a short and long pinion version, which adds a 50/50 chance of getting the incorrect version.
I see used Sterling's go for a couple hundred bucks all the time here in Illinois, which is about what a R&P is going to cost you. Go find yourself a good used unit and swap the whole thing. You'll likely end up with a newer/lower mileage version, you can (and should) check the condition and ratio, and you'll end up with a bunch of extra brake hardware, which could be handy down the road.
Good luck whichever way you end up choosing.
