Could you suggest good herbal supplements that help with anxiety, but don't cause potential liver damage?

Yes, possibly: Chamomile, passion flower, lemon balm, and theanine are a few that come to mind. Valerian and kava may be the ones you were thinking of with possible liver toxicity. In some people, st. John's wort might be useful -- even though it's more famous for use in mild-moderate depression. It's important for you to know that there are also very effective talk therapies for anxiety.