Are there studies on traditional Chinese medicine (TCM)?
Of course, and the studies are numerous. If conducted in non-Chinese contexts the results are most of the time quite underwhelming or more reason for concern than anything like "encouraging". Way too often the theory behind the treatments appears flaky, the evidence for effectiveness regarding desired results is weak and the dangers posed by unregulated and uncontrolled substances ingested looks quite big.
Has any proof ever been found for Qi energy?
None. TCM is very much incompatible with Western tradition of scientific thinking and explanation. What has been found, occasionally, is that despite a – from a Western viewpoint – complete garbage perspective concerning the underlying theory, some treatments offered by TCM appear to be effective. But remember that effective and efficient might be two different things here.
Many of the herbs, animals and metals employed are recognised to be pharmacologically relevant. That is 'active'; but often unproven to be more beneficial than detrimental.
If evidence based medicine oriented studies are undertaken, they analyse the effects of the herbs and other methods according to Western scientific standards, "Qi" is not featured there.
Someone offering a diagnose and selling a treatment in the way described in the question is not only highly unethical but also quite unlikely to be correct, even according to TCM standards.
One such study that examines TCM a style remedy for anxiety according to western standards (althogh not in humans) is
Antianxiety-like effects of Chimpi (dried citrus peels) in the elevated open-platform test:
Dried citrus peels (Chimpi) is one of the most common natural medicines with qi (energy flow) rectifying and shi (dampness) drying actions, which originates from Citrus unshiu, and/or C. reticulata according to the definition of the pharmacopoeiae of Japan and China. In this study, the pharmacological effects of their extracts and major chemical constituents hesperidin and its aglycone hesperetin on anxiety were examined with an anxiety model of elevated open-platform test using ICR male mice (6-week-old) and total duration of freezing was decreased in fluoxetine-treated mice, which is a simple and highly sensitive to the effects of serotonergic anxiolytics. Moreover, yokukansankachimpihange (YKH), a combination of yokukansan with Chimpi and Hange (Pinellia) was also examined because Chimpi is considered to play a crucial part in this formula against anxious symptoms in dementia patients. The results showed that Chimpi and YKH possess a significant anxiolytic-like effect similar to that of fluoxetine, suggesting that they might be similar to fluoxetine in their pharmacological actions through the serotonergic neurotransmission pathway. Moreover, it also suggested that the major chemical constituent, hesperidin could be an active principle attributed to the antianxiety-like effects with a direct and indirect role via its aglycone hesperetin.
Note the amount of weasel words and speculation displayed in this in vivo test. "Qi" is only mentioned as an organising principle with the originating system of medicine, the actual action displayed is then tried to be translatable into Western standard medical language and reasoning. The application of hesperidin alone, without mention of any 'Qi', is under very active investigation:
Sources to consider:
Helaine Selin & Hugh Shapiro: "Medicine Across Cultures. History and Practice of Medicine in Non-Western Cultures", Kluwer: New York, Boston, 2003.
James David Adams Jr & Eric J. Lien: "Traditional Chinese Medicine. Scientific Basis for Its Use", RSC Drug Discovery Series No. 31, Royal Society of Chemistry Publishing: Cambridge, 2013.
Kee Chang Huang: "The Pharmacology of Chinese Herbs", CRC Press: Baco Raton, London, 21999.
Chongyun Liu & Angela Tseng: "Chinese Herbal Medicine. Modern Applications Of Traditional Formulas", CRC Press: Boca Raton, London, 2005.
Kevin Chan & Henry Lee: "The Way Forward for Chines Medicine", Taylor & Francis: London, New York, 2002. (Esp. ch4: "Understanding the Toxicity of Chinese Herbal Medicinal Products" p 71–91.)