Write a short story centering on a person in the medieval era getting sick or injured and receiving historically accurate treatment from a doctor or surgeon and either recovering, dying or suffering. (Despite the lack of modern medical technology and wildly inaccurate medical "knowledge" with which they were working, some medieval physicians managed to describe and even treat some ailments correctly.) Sprinkle the story with details of what or how the people in medieval times worked, ate, dressed and did for fun.
Make a diorama showing a medieval physician in some part of the world -- not necessarily Europe -- diagnosing or treating a patient. For example, you could show someone being treated with leeches or bleeding. The goriness of many medieval medical procedures may make the diorama approach to such a project unappealing. But if you don't mind the gore and enjoy the artistic challenge of sculpting or modeling real-life scenes, a diorama would be a one-of-a-kind way to demonstrate your knowledge.
Pen a biography of a medieval physician or medical-text author, such as the Persian physician, author, mathematician, geologist and paleontologist Avicenna. The biography should include what is known about that person's birth, upbringing, education, work, influences, books and death. Also include information about the political, social, philosophical, cultural and even environmental environments that situate the person within the larger world. Highlight their medical triumphs. For example, according to an article in "Therapeutic Advances in Respiratory Disease," Avicenna correctly described major symptoms of asthma and tuberculosis.
Write up a fictional medieval patient's medical record in the style of a modern physician's notes, only using the methodology, terminology and treatments a medieval physician would have used to describe, diagnose and treat a patient. This approach to a medieval medical project is particularly well suited to people who feel uncomfortable with the creative aspect of a short-story approach or for people whose project guidelines do not allow for such a degree of creative latitude.