I nodded, not knowing why a doctor was speaking like this. But maybe these people were ill, and he was trying to cure them. There must have been medicine in his words—can there be medicine in words?
I think this can be a common mistake people make when learning the English language. Calling someone Dr. when they aren't really a doctor can be confusing. When Vuong mentions that "there must have been medicine in his words", it shows how powerful and healing MLK's speech was to the people in the crowd.