Depends on what writers need.
Yes, it's dull, but it varies with continuities. (for battle action at least, since obviously she screams a lot but isn't deaf 24/7)
In the current continuity, she's indeed auto-immune, as proven by Green Arrow Annual #1 (released January 2018). People go brain-dead walking towards the same direction, nobody is responding, and Black Canary is the only one unaffected, which makes her think it's got something to do with her hearing immunity.
Black Canary is immune to her own screams, and loud noises such as concerts, thanks to a thick membrane in her ears, shielding her eardrums. By immune, I mean both "not going deaf" and "not being mind-controlled by villain using soundwaves".
Two pages later, she goes against Vertigo.
Since she says "his frequency" (Vertigo's frequency), I think it's reasonable to think the two of them do operate on different frequencies, hence confirming that she's immune to other frequencies than her own.
However, that used not to be the case.
The comic Green Arrow/Black Canary #20 (2009) features Sean Sonus, a man Dinah accidentally rendered deaf years ago. He eventually engineers a device allowing him to hear again (by transmitting audio information directly into his brain). However, he's still bitter, and becomes Discord, using this same (sound-based) device to deafen everyone in the city.
Both Green Arrow, Black Canary and the counsellor they were meeting suddenly cannot hear each other. They first wonder if everyone else became mute, but Green Arrow smashing a glass proves them they're deaf, Black Canary included. It's then plausible that Canary did not have shielding-membrane protection in this continuity.
Side note, there have been at least two other instances of Black Canary being faced with "sound manipulation" villains:
- one in Batman: The brave and the bold, where she is controlled by Music Meister (so, not really immune then). However, Batman figures that her scream can be used against Music Meister and tricks her into singing very high. And it works! Her scream breaks Music Meister's control. So, kind of a balance?
- some Black Canary VS Black Siren in the Arrow series. It's a bit ambiguous in this scene since the Canary Cry rather acts like a "push", a Force thing, and the whole "what does it do to the other's ears" is left aside. Still, they don't both go deaf, as far as one can tell.
I didn't include them at first since you tagged the question with "comics" and "DCAU", which they're not part of, but they might still be relevant(ish).