“Many of the residents here are not equipped for life as it is commonly regulated,” reflects the narcissistic, madly distracted yet profoundly cultured narrator Helen near the end of this captivating, strange novel by New York author Lynne Tillman (who writes novels, short stories and criticism). Least of all this clever ex-historian whom I took to be Tillman’s realisation of a postmodern successor to such endearingly digressive women as Winnie from Beckett’s Happy Days or Joyce’s Molly Bloom.

That said, our heroine most resembles Ronnie Corbett, who in his weekly monologues on The Two Ronnies would go off on multiple tangents before concluding apologetically: “But I digress.” Helen is like that: a digressive flaneur through a mindscape seething with fixations on chair design, textile manufacture, the Zulu language, Kant’s account of mental ailments, how parasitical fleas prey on kittens in Amsterdam and lots more. Helen reflects repeatedly on one of the Manson murderers, Leslie Van Houten, seeing in her fate, perhaps, something of America’s capacity for evil and refusal of redemption. She also obsessively recalls her mum killing her beloved childhood cat because the cat killed Helen’s parakeet. Unlike Ronnie Corbett, though, Helen never stops digressing long enough to find time to apologise for her self-indulgences.

It’s not clear where the novel unfolds. Is Helen in rehab, a psychiatric institution, spa or east-coast retool of the Hotel California? Quite possibly she’s in a postmodern New England simulation of the sanatorium in Thomas Mann’s The Magic Mountain, where posh inmates turn out to be suffering not so much from physical ailments but seeking respite from the awfulness that is 21st-century America.

Helen, like Elizabeth Taylor’s Mrs Palfrey at the Claremont, readily assimilates this preposterous-sounding joint populated by perfunctorily described and mostly nameless eccentrics whose idea of post-dinner entertainment is a staged reading of the unwritten correspondence between Franz Kafka and his fiancee Felice.

Helen even contemplates sex with one of these shadowy inmates whom she calls the Count. He is, she tells us, “a bitterly provocative man, whose active disdain for common things and a love of evil might have carried the day and myself to his bed, briefly”. That said, the prospect “feels athletic and tiring, as if we’d played sex against each other in the Olympics”.

This is a woman, one feels, so hobbled by her unstoppably roving imagination that she could talk herself out of anything and then back into it again. But what ultimately decides her against an affair with the Count is something key to the novel. His skin. It is rough with large pores and there are blackheads around his nostrils. Deal-breaker!

For a woman who spends many of the novel’s 359 pages describing her complicated skin care regimen and disdainfully diagnosing the moles, rashes and psoriatic encrustations of fellow residents, the inadequately moisturised Count is clearly not a suitable sexual partner.

Instead, she has a hotel room quickie with the gauche young kitchen helper whose largest organ (which, as she repeatedly tells us, is the skin) proves to be just lovely.

Helen’s dermatological fixation figures in American Genius as an allegory of our hypermediated, death-denying age. The sensitivity of Helen’s skin reflects how impossible (and paradoxically desirable) it is to live as a sensitive soul, with your psychic borders incessantly breached by forces – history, other people, memories of dead cats – beyond your control.

But the skin trope is also to do with America. In one passage, Helen recalls teaching the historian Frederick Jackson Turner’s discredited frontier thesis, whereby his nation’s character was moulded by its westward expansion, giving that oxymoron, American civilisation, a roughness unlike that of its European forebears. That thesis, for Helen, encodes the desire to reincarnate in fresh new skin. Helen writes of “the common but unique American fantasy of life as an entirely different person with a virgin’s body whose hymen, a membrane of thin skin protecting an essential orifice that… is also just another frontier”.

The moral? America’s genius lies in convincing itself that its civilisation is not barbarous, that its frontiers must be shored up, ideally with walls to keep out the pet-eating other. And, most of all, that it can be born again, each time with a skin as blameless as a baby’s bottom’s.

But all that would be to impose a liminally limiting thesis on Tillman’s glorious gallimaufry of one woman’s antinomian tastes and outre obsessions. Like Joyce’s Ulysses, American Genius takes place over a single day; unlike it, very little happens. Helen takes breakfast, pours the delivered lunchtime tomato soup down the toilet and later has dinner. The drama is all in the mind.

Near the end, though, something happens. Helen leaves this nameless asylum to rejoin the real world. And in particular to visit her ailing mother. The contrast is poignant: on the one hand, an oversensitive, self-obsessed daughter whose life seems, at least to me, unbearably charged and raw; on the other, a mother losing her mind, increasingly insensitive to the real world. Tillman doesn’t push the moral, but after such a long book about a woman consumed by her obsessions to the point of madness, it’s difficult to decide which is the worse fate.

• American Genius, A Comedy by Lynne Tillman is published by Peninsula Press (£12.99). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply