In his Six Memos for the Next Millennium, Italo Calvino declares that with writing, unlike talking, he can revise until he is, if not quite satisfied, “able at least to eliminate those reasons for dissatisfaction” that he can identify. “Literature … is the Promised Land in which language becomes what it really ought to be.”

Sea Monsters is Chloe Aridjis’s third novel, following Asunder and Book of Clouds: a coming-of-age story set, for the first time, in the Mexico in which Aridjis grew up, in which the language is precise, strange, evocative and wise. It’s language as it really ought to be – from the descriptive metaphors (“The waves’ upward grasp. A boat in the distance, its throat flashing in the sun”) to a moving depiction of missing-dog posters (“These posters would start out vivid, inked with the owner’s nervous expectation, but as the days went by the hope and colour would be drained from them”).

The dogs aren’t all that’s missing: the narrator, 17-year-old Luisa, has run away from her home in Mexico City with a 19-year-old named Tomás Román. Sea Monsters is set in the late 1980s and opens with Luisa and Tomás at an Oaxacan beach called Zipolite. Her parents are loving, even benign, and she barely knows Tomás, so what is she playing at? “At some point I would have to explain to myself and to any witnesses how it was that I had ended up in Zipolite with him,” Luisa says, and then the novel leaps back in time to when she meets Tomás.

She first sees him from a distance. Dressed all in black, tall, slender, he gives a coin to an organ grinder, then keeps walking. She’s intrigued enough to follow him until she has to backtrack to catch the bus for school. The school is mostly populated by the sons and daughters of industrialists and politicians, and Luisa, the Joy Division-loving daughter of academics, feels adrift. Her friends are the sort of kids inclined to hang out in an abandoned, earthquake-damaged mansion: “the perfect place to smoke cigarettes and pose for imaginary album covers”.

When Luisa and Tomás chat briefly, it is all she needs to turn him into the object of an obsessive crush. She fills the margins of her school notebooks with his full name, Tomás Román, “the name blowing up genie-like as I tried out different scripts, cursive, feral and humdrum print, but after so many hours I’d tire of seeing those ten letters … that with repetition should have worked some manner of spell, yet instead lay silent, coffined, on the page.”

Driven by the ingenuity of youthful infatuation, she finds more ways to spend time with him. But he doesn’t talk much, nor is he particularly affectionate – there’s not much substance to Luisa’s crush, and she knows it. She listens to the Smiths after one of their ersatz dates, and, with the music-induced “spike in longing”, she decides that “more had to happen with Tomás, something had to be sealed, there had to be a sense of complicity”. That “more” comes along when she reads about Ukrainian dwarfs who have fled a circus, and are thought to be on their way to Oaxaca.

It turns out that Tomás loves Oaxaca, especially Zipolite, and Luisa proposes that they go there to find the Ukrainians. He agrees. It’s an indication of how young, immature and self-centred Luisa is that, on this thin premise, she leaves without so much as a note for her parents, to whom, she knows, her disappearance will cause great pain.

Meanwhile, it’s hard to tell how Tomás feels about all this, as he remains elusive, almost more a projection of Luisa’s inchoate longing than a person. In fact, Luisa aside, none of the characters ever fully comes to life – which, in a book concerned with the self-absorption of adolescence, feels eminently plausible.

Luisa devotes more time to rereading Baudelaire and figuring out which Walkman tapes she’ll take on her trip than she does to her parents’ plight, or to really getting to know Tomás. She’s full of longing, but she hasn’t quite figured out for what; she’s avid to escape, but she’s not sure where to. In the meantime, music and poetry are pointing the way. In an indelible scene on the Zipolite shore, Tomás calls her attention to a cluster of palms. “I’ll race you to those trees,” he says. She starts outstripping him, at which point he, without warning, turns around. He runs at full speed in the opposite direction. He’s ceding the race he was going to lose anyway; she’s won, but what has she won?

The novel poses far more questions than it answers, and it does so accurately and beautifully.

• RO Kwon’s The Incendiaries is published by Virago. Sea Monsters is published by Chatto & Windus (£12.99). To order a copy go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £15, online orders only. Phone orders min p&p of £1.99.