Louise Bourgeois working on Sleep II in Italy, 1967. Photograph: Studio Fotografico, Carrara /The Easton Foundation

Above Freud's bulbous, oriental carpet-draped couch in 20 Maresfield Gardens, Hampstead, hangs a shrivelled, double-headed bronze penis by Louise Bourgeois. In an essay on "Freud's Toys" (1990), as Bourgeois dismissed the ancient artefacts that swarm over his desk and shelves (including numerous phallic amulets), she described Freud's cluttered office, with its "half-dead hysterics", as "a pitiful place". She also referred to Freud's patients as "maggots", which gives additional resonance to the placing of her suspended larval form. Analysis was, in her view, a form of metamorphosis, promising the transformation of seething misery into what Freud described as "common unhappiness". "A maggot," Bourgeois wrote, "is actually a symbol of resurrection."

Though she doesn't acknowledge it in her essay, Bourgeois had been in analysis herself for more than 30 years. In 1951, suffering from depression after her father's death, she entered therapy with Dr Leonard Cammer. The following year she switched to Dr Henry Lowenfeld, a second-generation Freudian who had emigrated to New York in 1938, the same year she did. Lowenfeld had been trained by the Marxist analyst Otto Fenichel in Berlin, where he was also a part of Wilhelm Reich's radical group, Sex-Pol. However, in New York, keen to assimilate to American culture and disenchanted with communism, Lowenfeld became part of the psychoanalytic mainstream and hid his radical past. At the height of the cold war he stole the incriminating Rundbriefe – letters written by Fenichel in the 1930s and circulated among their group of dissident analysts – from his colleague Annie Reich in an attempt to erase that history.

In 2007, just before Bourgeois's retrospective at Tate Modern, two boxes of discarded writings that refer to her analysis, which she underwent four times a week, were found in her Chelsea home; after her death in 2010 (aged 98), her assistant unearthed two more. Selections of these have been exhibited in the Freud museum alongside two dozen of her bulging and sinister patchwork sculptures and installations. These jottings, on random pads, letterheads, even playing cards, offer a glimpse into Bourgeois's psychological states. According to these notes, Lowenfeld considered the artist's inability to accept her aggression as the central problem to be worked through in analysis. "Aggression is used by guilt and turned against myself instead of being sublimated into useful channels," she wrote.

To art historians her free associations and doodles not only suggest clues as to the personal relationships and conflicts that inform all her work, but seem to offer direct links to her creative process (one Isis-like sketch is displayed here next to a similar multi-breasted sculpture, as fecund as the Venus of Willendorf). In an aborted letter to "Mon cher Papa", Bourgeois wrote: "In the 20th century the best work has been produced by those people whose exclusive concern was themselves." Her father was a tyrannical philanderer who had a 10-year affair with a live-in English governess, the discovery of which was the central trauma to which Bourgeois endlessly returned in her confessional work.

The recently discovered archive reveals the artist to have been an enthusiastic list-maker. In 1958, aged 47, Bourgeois compiled a melancholy account of her failures: "I have failed as a wife / as a woman / as a mother / as a hostess / as an artist / as a business woman", and so on. She made a suicidal list of "seven easy ways to end it all" (and throws in another for good measure). She listed her fears: "I am afraid of silence / I am afraid of the dark / I am afraid to fall down/ I am afraid of insomnia / I am afraid of emptiness …" And her feelings about analysis: "The analysis is a job / is a trap / is a privilege / is a luxury / is a duty … is a joke / makes me powerless / makes me into a cop / is a bad dream …"

Many of her automatic writings resemble concrete poetry, such as one arranged as a spiral of injunctions: "Do not risk too much / Do not hide too much / Do not neglect too much …" Others, written in cramped lines, are reminiscent of the webs of psychic "tangles, fankles, impasses, disjunctions, whirligogs, [and] binds" that RD Laing formulates in Knots (1970). Bourgeois asked: "What is it that you want / do you know what it is / is it possible? no, why not / are you looking for a substitute. why? / which one?" On another loose leaf she wrote: "To be hurt / fear to be hurt / to hurt before you are hurt / what hurts?" (She answered her question by reverting to more list making: "to be abandoned / to be criticised / to be attached / to be asked too much / used / to be refused …")

These emotional inventories, with all their tangled logic, were Bourgeois's way of thinking, of working through. It was the art critic Peter Frank who encouraged her to jot down these free associations, not Lowenfeld: "It is not either my medicine nor my duty," she wrote in reference to Frank's suggestion; "I write because I have always felt that if people knew me really, they could not fail to like me. I write or make sculpture to be loved (for what I am)." Bourgeois admitted that this was a lost cause and was dismissive of their worth, suggesting that their meaning immediately evaporated, like Chinese calligraphy brushed on to stone with water: "Tout de mes notes seems remote + foreign except when in the process of being written, they communicate nothing not even to me."

Bourgeois considered art as her parallel "form of psychoanalysis", offering privileged and unique access to the unconscious, as well as a form of psychological release. On a piece of pink paper she scratched the slogan, "Art is a guarantee of sanity." Her artwork was reparative, a form of mental mending. Bourgeois's mother had been a tapestry restorer and Bourgeois often compared her to a spider spinning a fragile web; Maman (1999), Bourgeois's massive arachnid guarding an egg, is on display in the garden of the Freud museum (where Anna Freud's sizeable loom sits upstairs). In her textile pieces, the artist follows in her mother's footsteps by weaving, a craft that Freud, in one of his wilder hypotheses, thought had been invented by women as an unconscious product of "penis envy" (because the results imitate the hair that hides the genitals).

Bourgeois identified herself as a hysteric and made sculptures, like Arch of Hysteria (1993), that made reference to the "whirlpool of histeria" (sic) in which she often found herself consumed. In the Freud museum exhibition, the engraving that usually hangs above the famous couch – depicting Freud's mentor, Jean-Martin Charcot, the "Napoleon of the neurosis", demonstrating hypnosis on a swooning hysterical patient – has been moved to an adjacent room, where it serves to introduce works by Bourgeois. In that context, the accompanying vitrines contain what looks like outsider art by an inmate of the Salpêtrière Hospital: magical objects with multiple faces; patchwork dolls with amputated limbs over which knives hover threateningly.

The artist was well-versed in psychoanalytic concepts, which informed and have often been used to help understand her work. She frequently annotated the psychoanalytic writings she read; on display here is her summary of a case history recounted in Werner Muensterberger's "The Creative Process: Its Relation to Object Loss and Fetishism" (1963). Muensterberger tells the story of a grieving woman who made a doll out of her late husband's dirty underclothes, a mannequin she tucked up next to her in bed, which evidently fascinated Bourgeois. Her husband, the art historian Robert Goldwater, to whom many of Bourgeois's notes refer (did he desire her anymore?), was the director of the Museum of Primitive Art in New York and would have shared her interest in such fetish objects. Her own work was a similarly magical act aimed at exorcising trauma.

But, ultimately, Bourgeois felt that analysis had little to offer the artist. "The truth is that Freud did nothing for artists, or for the artist's problem, the artist's torment," Bourgeois wrote in "Freud's Toys", as if in frustration with the process to which she submitted for so many years, "to be an artist involves some suffering. That's why artists repeat themselves – because they have no access to a cure." Lowenfeld had died four years earlier, ending her analysis but evidently not her pain, which continued to fuel her work. In his essay "Dostoevesky and Parricide" (1926), Freud himself admitted: "Before the problem of the creative artist, psychoanalysis must lay down its arms."