BY the time I meet Nina Nesbitt, I am a little bit in love with her.

This fact in itself makes me a Nesbian (that's right, Nesbian); but her new single, Selfies, has also set up camp in my head - and it won't leave. Kind of like the last guest at a party who outstays his welcome till 4am, except in a good way, Selfies is incredibly catchy. And Nesbitt, when I meet her before its release, comes off as astonishingly poised, in both senses of the word: a composed, self-assured young woman who appears to be on the brink of something big.

At only 19, Nesbitt has accrued over 133,000 Twitter followers; garnered an army of loyal fans (my fellow Nesbians); and clocked up more than 20 million YouTube hits since she began posting videos of her self-penned songs and chart covers as a teen growing up in Balerno, Edinburgh. She has also played some considerably large gigs - not least to a sold-out crowd in New York City last year, most of whom seemed to know the words to every song - all before releasing a debut album. The appropriately entitled Peroxide, named in part because of her face-framing blonde mane, is out this month.

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In fact, her hair is the first thing I notice when I walk into the basement cafe where we're meeting in Glasgow. She's 5'8" and very pretty, with big almond eyes emblazoned with lashings of liner and mascara. Until recently, I knew her best from her biggest hit to date, the infectious Stay Out. But I now have Radio 1 to thank for my current earworm. I tell her this as we sit down for a chat - that I love Selfies.

"Aw, thank you," she smiles. "It's a bit of a departure from what I've done before. I don't want to be a folk singer-songwriter. I get bored sticking to one genre, so I wanted to do something a bit different."

If by that Nesbitt means a song that is undiluted delicious pop, she has succeeded. A break-up song for its time, Nesbitt sings about a boy who has dumped her and how she is posting happy selfies (hand-held self-portrait photographs) to pretend all is well. It is not to be dismissed as a vacuous teen tune trying to shamelessly tap into the word of the moment; Selfies is sharp. And that's down to Nesbitt's talent for songwriting. While some tracks on the album - like the foot-stomping Mr C - are reminiscent of Amy Macdonald, Selfies's shameless likeability is more akin to Taylor Swift. Nesbitt's lyrics speak sassily and smartly to her demographic - mainly teenage girls, for now - but then The Hardest Part, her favourite track, comes out of nowhere as the finale, achingly mature in its sentiments and depth, and beautiful in its paired-down simplicity.

"It's always been more about the words than the music," Nesbitt explains, her voice rising with this last word in typical teenage inflection. "I said the other day that when I was making the album, I wanted to create a story instead of a sound. My strength is lyrics. It's what I'm naturally more inclined to do so I don't really have a genre or a style."

She throws these latter words off her tongue like they're negative. But she's right: it is hard to pigeonhole her. She herself is inspired by such opposites as Taylor Swift and Debbie Harry; and, early on, realising she wanted to do more than pop, decided against The X-Factor route. Now, on the verge of her album's release, Nesbitt says she's feeling good, but nervous. She didn't want to rush Peroxide - she enlisted the help of producer Jake Gosling (Paloma Faith, Ed Sheeran) - and it shows.

"I try not to think about it too much. I keep listening to it in the car and thinking, 'Is it good, is it not?' But I'm really pleased with it. You look at other artists and they've all had [a particular] hit and then they have the album out. And I don't class myself as having a hit. I'd rather make a body of work and put it out than just have a one-hit wonder."

Nor does she see herself as being on the verge of a moment. "I don't think about it. It's been such a gradual thing for me that it's never been like an overnight X-Factor thing. I don't want to expect anything because I don't want to be disappointed, but my ambition is to hopefully play to as many people as possible and tour around the world."

Nesbitt is down to earth, yet determined to shoot for the stars; modest, but overwhelmingly ambitious. An only child from a non-musical family whose parents did "normal jobs", she has her pragmatic and cynical Scottish father to thank for keeping grounded, her Swedish mother for urging her to follow her dreams rather than the more predictable university path. Both, she says, have been incredibly supportive. Her mother lives part-time with her in London.

As a child, she liked to write stories. "I picked up a keyboard at 10 and I played little chords and put the stories to songs," she recalls. But it wasn't until she picked up a guitar at 15 that everything gelled. Self-taught, she decided she wanted to become a singer. Until then, university was the plan; but then she started posting on YouTube - and the views kept clocking up. She smiles remembering this like it was so long ago and says: "I thought, 'I'm from Balerno, it's not like I'm from London. No-one's ever going to find me.' Then it grew really slowly. It's been one thing after another."

But the big break was arguably from Ed Sheeran. The pair were linked as a couple in the past - much to Nesbitt's annoyance - although neither has ever confirmed it. If her song The Hardest Part - about the bittersweet sadness of a relationship that cannot be - is about Sheeran, I'm certainly not going to ask Nesbitt today. The only glimpse I get that there could be history between the two is when I mention his name: her eyes instantly fall to her lap. But Nesbitt's love life doesn't interest me. I want to know if the story about how Sheeran discovered her at 16 is really true.

"Yeah," she confirms, with possible relief. "My friend worked at the radio and she was like, 'Come and see this guy' and I was like, ok. I loved his music ..." He asked her to play a tune for him just moments after they met, in public, in an upstairs bar in Edinburgh. "Then I started to tour with him. It was random but good exposure."

Prior to that, she would play at Edinburgh's Electric Circus some weekends. "I'd have, like, a little sheet of paper with me and my guitar, and I'd look down and not talk to anyone," she recalls.

Nesbitt caught chart-topping musician Example's attention after Sheeran showed him a video of her doing a cover of one of his songs. He tweeted it to all his followers,and a tour soon followed. "Getting the opportunity to support Example on an arena tour, just me and my guitar in front of all these ravers - you move out of your comfort zone and learn how to play to a crowd. It was like a fast track to confidence."

So where does she see herself in five years? "I'm nowhere near where I want to end up at the moment," she says sweetly, but with a grin. She'd like to break America, do something in fashion, maybe a bit of acting. "I'm one of those people that are never fully contented. I always want the next thing. If it's the Usher Hall, I want two nights at the Usher Hall. I always want more. That's probably not great but at the same time it is why the ambition is there - because I just want to be as big as I can be."

Peroxide is released on February 17 on Island Records. Nina Nesbitt plays the Usher Hall, Edinburgh on March 23