Christina Lunka appeared nervous and excited as she sat in the Chinese herbal therapy center recently opened by the Cleveland Clinic. The 49-year-old had been to many doctors seeking help for ongoing issues that included joint pain and digestive problems. Now the Kirtland, Ohio, resident was hoping to find relief through herbal remedies. "Do you have something for inflammation?" Ms. Lunka asked herbalist Galina Roofener during a one-hour consultation. "Absolutely," responded Ms. Roofener. "This is for pain, for digestion, for inflammation, all of the above," she said, handing Ms. Lunka a bottle with capsules of an herbal combination called Xiao...