Tickets for his East Neuk Festival concert sold out so quickly the organisers promptly booked him for a repeat performance.

The repeat performance sold out. It's the kind of box-office rush you might expect for a big-name soloist – but for a 20-year-old classical guitarist who has released no recordings, who has no agent, who is technically still a student?

Meet Sean Shibe. Within a month of graduating from the Royal Conservatoire of Scotland he'd made his Wigmore Hall debut in London and given a sold-out Brighton Festival recital. Before the year is out he'll have featured at the East Neuk and the Lammermuir festivals, and played concertos with the Scottish Chamber Orchestra and BBC Scottish Symphony Orchestra. When Michael Tumelty heard him perform at a student concert some three years ago, The Herald critic pronounced him "the finest acoustic guitarist I have ever heard - Remember the name. One day he will be famous."

In person Shibe has the breezy confidence to handle the hype. He arrives for our interview with a rucksack full of laundry (his washing machine's broken) and a justifiably cloudy head (it's the morning after his final undergraduate recital). He's relaxed company as we venture out into Kelvingrove Park for a photoshoot, unfazed by the photographer's requests to lie in the grass with buttercups scattered around his head. When she asks him to pose in front of the dilapidated Kelvingrove Bandstand, he fixes a steely gaze into the lens, then laughs at his own seriousness.

The interview proper begins on a more downbeat note. Shibe is tired. He wonders out loud whether he has bitten off more than he can chew this summer. "Without an agent," he explains, "I have to book all my own travel, deal with my own expenses and figure out all my scheduling. Check this out -" He points to a diary week scribbled black with logistics. "I've taken to writing things in my diary, like every month I go to the toilet and every six months I have a shower -"

Shibe was born in Edinburgh to Scottish-Japanese parents who run a pottery in the city's south side. There was music around at home –"my dad played guitar: old coal-mining songs, anti-Thatcherite songs" – but Shibe claims he was "a thoroughly non- musical child". "When I was seven, my mum walked past a string instrument shop on her way to the pottery. There was a guitar in the window and she got it for me. That was it, no story of marvellous inspiration or divine providence, I'm afraid." He joined an after-school guitar club at Sciennes Primary, and within a couple of years had been admitted as the only guitar student at the City of Edinburgh Music School.

Did he practise for endless hours at that age? "God no! I hated practising. I did half an hour a day, max. I was a normal kid." At 13 he transferred to Aberdeen's City Music School. There were other options, including an offer from the prestigious Yehudi Menuhin School, but Aberdeen had a trump card: Allan Neave. Shibe is unequivocal in his respect for Neave, with whom he still takes lessons. "Back then I knew it was his sound and his musicianship I wanted to learn from," he says, "and I was totally right."

The move north meant leaving home. Daunting for a 13-year-old? "Nah, fine," Shibe shrugs. Aberdeen's music school students shared a campus with the Scottish Agricultural College. "Us and the farmers," he says, "we were a strange, sometimes violent juxtaposition. They'd chuck beer bottles at us; we'd retaliate by egging their cars. All good high jinks."

During his fifth year Shibe auditioned for music colleges. "Why would I stay on at school to get Advanced Higher Maths and English if I knew what I wanted to do?" He was offered scholarships from Trinity College and the Royal College of Music in London, but chose the (then) RSAMD so he could continue studying with Neave. He arrived in Glasgow at 16, the youngest student the college has ever admitted. And it was there that the fearsome routine set in.

"I'd wake up at 5.45am and cycle to the gym. Coffee at 7.30am, head to the academy and practice. The building gets busy at about 10.30am, so I'd leave and come back at five or six in the evening and stay until 9pm. Bed by 11pm, rinse and repeat. It was an insane schedule, but the exercise and coffee worked - Hemingway used to talk about the juice of inspiration: well, exercise and coffee are my juice."

And that juice fuelled him through a raft of competition glory, including, in 2011, coveted first prize in the Royal Over-Seas League Competition and now a prestigious Borletti-Buitoni fellowship. But the long hours took their toll, too; Shibe worries about his posture, about back pain and muscle strain. "I've started getting strange tension problems that came from a period of practising eight hours a day. I need to find a physio and do some pilates." Another shrug. "My mother is more worried than I am."

The next move (well, provisionally speaking: there's the slight technicality that he hasn't actually auditioned yet) will be this autumn, to Graz to study with Italian guitarist Paolo Pegararo. Shibe explains the choice: "Fees for a Masters in America would be $30,000 a year at least. Fees in Austria are €17 a year – subscription to the National Union of Students. It's a no-brainer." Besides, friends have warned that he might have trouble in America. "Because of my mindset," he says. "Like, for example, when I received vitriolic messages from a Tea Party supporter after posting a memorial to Christopher Hitchens on my blog."

Shibe's blog, which he has kept since 2008, is intriguing. "A combination of my strange non-humour, concert reviews, political ranting," he says, and admits it's an unusually, possibly unwisely, candid public face. "If I'm a bit drunk I might put up a video of ducks being blown over in the wind, that kind of thing. I once wrote a post comparing famous guitarists to James Bond villains. I included some professors at London colleges and some of the German competition mafia - It was probably a good idea to take that one down."

There's plenty he's left up, though, and his sharp, sassy writing contrasts with the dry clout of his CV. He writes that he hates competitions, despite winning so many. He says he doesn't believe in a career – "you shouldn't think about how to build a career as a musician; you should just think about how to improve the music that you make, and if that goes well then you get a career out of it anyway" – yet he's stuffed his diary to breaking point.

And despite already being the most lauded British guitarist of a generation, he has no qualms in voicing serious doubts about the instrument's repertoire. "Guitar music is often very nice background music," he says. "I go to a lot of guitar concerts and often I find myself downright bored. I think a lot of that is down to repertoire. And if you're surrounded by second-rate music when you're growing as a musician then you're not going to develop as well as if you're surrounded by Bach and Beethoven. I don't think guitarists are the best musicians. I think there are a few great musicians who have become guitarists."

Shibe knows he's good: it's the self-assurance that comes through in every aspect of his playing. His finger work is percussive, deadly precise. His textures are dazzlingly varied, so well-defined it sounds as though several hands are plucking several sets of strings. His technical command allows him to stretch time, to play with colours, to really dare. On a diet of Dowland, Bach, Bream, Segovia, Britten, Takemitsu – Shibe's favourite composers for guitar – he has developed into a musician who commands you to sit up and listen.

But he also knows he's not infallible. "That exam yesterday went badly," he says, drumming his fingers on the table. "My playing was unclean and didn't have enough character. When I begin to play badly I stop taking risks, and yesterday I was playing badly because I hadn't had enough time with the music." He's flicking through his diary again, lingering over the emptier pages of July and August when he'll have time to reboot. Then it's Austria, more concerts, recording sessions. He looks up and grins. "You know what? It's great fun."

Sean Shibe plays Dunino Church on Thursday, 2pm and 4pm, as part of the East Neuk Festival (www.eastneukfestival.com). He will play Lennoxlove House, Haddington ,on September 18, 8pm, as artist-in-residence at the Lammermuir Festival (www.lammermuirfestival.co.uk).