Differential or wheel bearing???

Well your hot bearing is a good indication. Unless you have a dragging brake.
I had an off brand a while back, and the nose was a pitted carrier bearing. Not a big deal to replace, but it was on a hoist. And once carrier was out,the pitting was easily noticeable.
Outer bearings are flat rollers, you should be able to see the wear. If i recall, there are axle repair bearings available if your axle is scored.

I have a 7.25 to do in a few weeks too. Its out and on a stand so its easier to do.
I plan to pull it apart, then order the necessary bits.