Sounds just like mine did when the pinion bearing went. The noise came on pretty quickly. It was pretty noisy and would get quiet when I let off the gas. When I left Prescott for Phoenix, (second trip in a week) it was fine. That is 100 miles each way. By the time I got back it was really easy to hear. Here is what I did;
I removed the rear drive shaft, rear axles and the rear diff. I covered the diff and axle openings with wooden caps made on my saw and pressed the CDL switch. Then I drove away with front wheel drive like a really big Honda! I took it out on the highway to make sure that the noise was really gone with the rear end removed. It was.
In FWD, I drove down to my brother's shop in the city, carrying the diff in the back. We looked at it and decided to order a new pinion bearing. We got a Timkin bearing from Curt at Cruiser Outfitters that is stronger than the original. We are both old Jap auto techs, but neither of us had ever done any diff work. We were winging it in every way. Once the bearing was ordered, I drove back home with FWD.
Two weeks later when the bearing arrived, I drove back down. We rebuilt the rear end with a new pinion seal and a new crush sleeve. It was easy. Some of those who work on diffs for a living will act like it is rocket science, but it is not. We did not have to change any of the shims, or reset the backlash. We checked everything and set pre-loads at the high end of factory spec. We but it in a box and I drove back home where I installed it and put the axles and driveshaft back in. The only problem that we had was crushing the crush sleeve. We tried to tighten the pinion up with an impact, but ended up stripping the nut due to too much pressure. We were lucky in that a parts store had a nut from a Nissan front axle that fit perfectly. When you crush the sleeve, put the pinion and housing on the press and crush it almost as far as you want it to crush. Then tighten the nut and set the preload.
Note here that I logged 400+ miles over 2 weeks in addition to the driving that I did around home in FWD with the CDL engaged. It is not a problem.
The sure way to determine your problem is as I did. I serviced all of the wheel bearings since they were overdue anyway and a wheel bearing will make a noise similar to a pinion. Then I removed the rear end and the noise went away. With a fresh rear diff, the noise is still gone.
My brother, by the way, is toolsrus on this site. If you have questions, PM him or me.