Benzos are known to be ototoxic, and have greater effects the higher the dose you are placed on.
I've been on a very small dose of klonopin (0.5 mg per day) since May to control panic attacks.
I have a long way to go to figure out which of my medications has worsened my inner ear health, but I can tell you the least likely of these is the klonopin ( a benzo) that I have been taken. I have also never personally experienced a change in hearing or a tinnitus spike as a result of being on the drug.
If anything, reducing the number of panic attacks (by like 80%) has saved me from episodes of tinnitus spikes or sudden hearing loss that were directly caused by panic attacks and the effects they had on blood pressure and stress hormones.
Depending on the severity of your anxiety, getting control even through the prescription med route may far outweigh the negative health effects of the anxiety itself (including in your ears!).
I would research other potential medications or options to treat anxiety in consultation with an ENT or an neuro-otolotist if you have one along with your psychiatrist, but taking a very small dose of one of the benzos for a short or mildly long-term period may be an option while you find other ways to reduce your anxiety.
Of course, some benzos, particuarly valium, also have addictive properties and withdrawal effects, so that is another thing to factor in when considering a benzo.