I started out in office support but at the same time doing loads of coding before I moved exclusively into development. So I was constantly interrupted about inane things (e.g. A4 Load Letter!). I developed the skills to work in busy environments, a number are mentioned in the comments.
Take note of the forced interruption - take a damn break! It's plain unhealthy to get so into something like that at your desk. If you go for a walk, you're less likely to be disturbed if you need to do some thought work! What about your whiteboard? Well I work a lot with remote people/teams where whiteboards are usually impractical, so it's possible to survive without the high from the pens!
Reading previous comments, I have 2 bugbears to raise...
1) Don't blame Agile. It's only there to help keep you developing things that are relevant. If there's something wrong with your processes, change them! That's what retro's are for! Sounds like everyone's main complaint is "I spend ages diving down rabbit holes of complexity because we never fix tech debt" - does your business really think that's a healthy situation in which to work?
2) Headphones.. if used properly are great ways to work, and I'm sure some people may work better with them. But they are also misused quite frequently. When I've heard trainees upset and crying because they can't get the help they need because their assigned senior is always plugged in and is unapproachable... you gits! I've also observed great amounts of sloppy working from headphoners too, like the ones who never seem to use the right processes, who create enormous PR's so complicated that they're un-reviewable, who end up getting sacked because they're unmanageable and unproductive from the business' point of view, etc.
I would also say that if you are one of those works with their headphones on, beware! The new generation will kick your butts with their collaborative working skills. Which, I might say, generally produce things far better than the lone wolf developer. If you are paired with someone and you get interrupted, chances are you'll pick up the trail a lot quicker.
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