Before you change your gears, make sure that it isn't just a u-joint. It could easily make the noises you describe. As far as the burn-out went, if you do not have true posi-traction, more power could be going to the wheels unevenly! However, if you try it several times, doing the burn out a different ways, and the same axle never ever breaks traction, that could be a sign of $$$ needed to be spent on new axle(s).
Put the car on jack stands, the rear, and do it safely (to avoid death). with the wheels off the ground , wiggle each wheel, independently, and see if you can tell if there is unusual "play" or slop in it. If 1 is F**kd up, it will feel diff from the other.
If either are compromised, it could abnormally wear the rear gears and cause a drone sort of noise, that over time gets worse and worse, eventually leading you to change out gears, which could be a good thing.

That's how it happened to me! Now, while you have the car on jack stands, take a look at that driveshaft, at the u-joints, that could be the culprit. Much luck to you my friend!