Character Analysis
Ernst Fleischl von Marxow was a senior colleague of Freud's at Ernst Wilhelm von Brücke's Institute of Physiology. Freud "greatly admired" Fleischl (source). In fact, as one scholar puts it, Freud "took [Fleischl] as a model and almost worshipped" him (source).
Well, Fleischl was addicted to morphine, which he had begun using as a painkiller after an amputation when he was twenty-five years old (source). Because Freud was in the middle of early research into the pain-killing properties of cocaine—and because the medical profession hadn't yet realized that cocaine was an extremely addictive drug—Freud recommended that Fleischl begin using cocaine rather than morphine (source). Fleischl became addicted to the drug and in 1891 he died of an injected overdose.
For these reasons, when Fleischl appears in Freud's dreams, he is sometimes associated with Freud's feelings of guilt, anxiety about his professional competence, and desire to be held blameless in the face of potential accusations of medical malpractice.
For this reason, Freud associates certain elements of his Dream of Irma's Injection (2.1.16) with the recommendation that he made to Fleischl (2.1.24, 37), and Freud scholars have argued that in the dream, Freud's "guilt over Fleischl's injections became connected with his feeling that once again, now in the case of Irma, he was being blamed for recommending a solution which was not good" (source).