It would depend on the type of anxiety, the symptoms. Some anxiety worsens with repetitive prayer. As much as I believe in the power of prayer for healing I also agree with some of the finest theologians: doctors, therapists, healers are here to help us too. Be thoughtful and discerning about your healthcare and do pray for your healthcare provider as well as others afflicted with anxiety.
St Dymphna is an interesting saint for mental afflictions.
Also St. Gerard is underutilized and his life is incredibly inspiring. His faith and miracles were truly humble and powerful.