Teacher Health and Wellness Act This bill directs the National Institutes of Health to carry out a five-year study on reducing teacher stress and increasing teacher retention and well-being by implementing and analyzing the results of any of several types of innovative approaches that include: workplace wellness programs; social emotional learning programs; teacher stress management programs; mentoring and induction programs during the school year and teacher pre-service; organizational interventions such as principal training programs; teacher residency programs; complementary health approaches, such as mindfulness meditation; and school reorganization.