did you have any oil stains on inside the wheels ?
my 2011 made noise like you describe and ended up being axle seals busted and leaked out most of the diff fluid
and high pitch squealing noise came from that oil burning up on the brakes at speed . bearings would make a whining noise kind of like a tornado siren at distance .

i ended up doing the work myself it took close to 5.hours start to finish . Most important thing is carefully removing friction plates clutches discs things from differential and making sure things don't go falling out on you and you don't know the order they were in . then.. . there are C-clamps on the axle on inside ends being held split apart buy a S-clamp Those are a Pain in the *@! to get out and the seals are some Tough soB's hard to get out seal puller i had was bending i had to brake them loose with a steel punch but risking damage to axle housing .
so.. . i would find a good write-up on it and study the hell out of it and/or have some help
once the axles are out you can check the axles and splines and bearings and all that's in the diff
but the job should not cost that much that's just... .
AnyWhoom good Luck with it n'stuff.. .

I'd honestly probably lean to have them do both at once. My 2005 wore a bearing and seal on one side, and when they got into both axles were scored. And the rear end had been totally replaced on that car while it was in service (I managed to get the service records from the dealer with a letter from the sheriff's dept, go figure).

Looks like 31 spline axles are running between 150-200.

2003+ the axle shafts can be hardened or not as quality control is bad. 2010 was another bad year for axle shafts.

The reason the shafts fail in police use is that often the patrol cars sit on an un-level terrain. When a speeder is identified, often the officer slammed the pedal to the floor which all the fluid is on the opposite side of the axle tube. Do you ever wonder how a taxi can make 300-400k on just a simple axle service and maybe some bearings here and there?