Yes, anxiety and extreme anxiety is quite common during withdrawals. Benzos are extremely addictive themselves and act in a very similar fashion to alcohol so I would strongly recommend you only take them under close supervision of a doctor that knows about your drinking. It’s actually never a bad idea so see a doctor before quitting cold turkey anyway as there are thighs far worse than anxiety that can happen during withdrawals. Not common but definitely possible.
I know that last time you were here you went through a very similar scenario when you attempted to quit. And you left here feeling that your other meds were the problem all along so you decided to moderate your drinking again. I hear you saying that you have decided to quit for good which I think is the right choice too, please be safe about it.