What is act therapy for anxiety? is it clinically and medically proven?

I find it very good: Most psychotherapy types can not be consider 'proved' but there are studies that compare outcomes. This like may be helpful to you. The most important thing is that you feel that it makes sense and that you can trust and respect the clinician. If you can, give it a trial for a few sessions to see. Again, you are the best judge. I fully support your idea that this vs drugs is a good anxiety tx.