I take metoprolol which is a similar beta blocker. It helps attenuate the physical anxiety symptoms. Without it I would get more anxious because of the physical feelings of anxiety and it was harder to get my mind off it when my body kept reminding me. Now my anxiety doesn't feel quite as overwhelming.
I'm in the same boat with benzos... Almost 6 months sober from alcohol so benzos would be a terrible idea. Some other alternatives for anxiety are SSRIs, Buspar, and gabapentin. If your doc hasn't mentioned them then they might be worth bringing up.