I do feel your pain. I have Hyperacusia and Auditory Processing Disorder. It affects not just in the office, but all day long.
Trying to sleep in noisy neighborhood seems impossible to most of people, but I soon realized that I really was under average. Even getting rid of noise, my brain was always in a loop trying to detect the next annoying sound in the new environment sound threshold, such as dog barking blocks away.
The very same for car horns. I only feel comfortable with a background white/pink-noise sound-like.
I recent went through the same issue in my work, a small company working in the same room, with often uneducated noises, topics and discussions about other projects reaching everyone in the office. I can't say just one attitude can solve your problem, but a mix of them.
The solution goes to two different paths: Active and Passive attitudes.
Talk with HR and/or your boss about your problem, how does it affect your productivity and how much company would win also with a solution for you. From my experience, they will give a sh** if you no offer a loose-loose problem with a win-win solution. Probably, you are shooting yourself in the foot.
As you've said, you already had this discussion, let's jump to next option.
"this isn't working for me": this is crystal clear and self-explanatory. The company does not fit for you. Just like that. It's very important to get from your perspective and not "I'm not fitting in this company" as you are the fish out the water. You just need a place where you are happy and you are comfortable.
I imagine you are looking for a solution without jump into this final one as you're new in the job, but I'm afraid the company culture does not permit that.
- Headphones. Good ones. With noise-cancelling. I bought recently a Bose QuietComfort 25 which I don't regret at all despite the price. It worth getting one with similar quality with no doubt. Think about your health, your quality of life. I use every day and I let everybody know that they can reach me anytime. You don't need to listen music, most of times just the noise-cancelling active. Often music doesn't help too, mainly the singed, try instrumental, such as Classical, Soundtracks and New Age/relaxing musics.
It also promotes conversations by Skype or email, and IMHO I consider it better as it makes everything documented, due to nature of communication; clearer, because one tend to make himself clearer to compensate a more formal not face-to-face communication; productive, as it isn't task-blocking (one can finish what you're doing right now and/or think a bit more before respond to communication).
Don't ever, never, niemals use earplugs, earphones or earbuds. It gets easy to use them in a unhealthy way. Even standard cheap headphones led me to tinnitus, in part due to lack of sound isolation.
- While trying to solve your specific problem at work, I highly recommend to try to solve your condition too. I suggest you to take Brief or Cognitive Behavioral therapy. Please don't take me wrong, people are more far to perfect than they try to seem to be.
*For the sake of simplicity and clarity, I'm going to assume that every statement is true, e.g. your colleague said the truth regarding the reason you were relocated. For the same reason I'm going to suppress adverbs, creating some generalizations.
When I first got here I had a solitary corner office where I kept the door closed to work in silence. I ended up being moved to another office with a new colleague. He's resisting closing the door and mentioned that I was actually moved because I always closed my door.
That sounds a disastrous way to solve your problem. But it seems also that they are being rebuked indirectly because you represent a problem that they don't know how (or don't want) to deal.
I explain how noise is a medical issue for me and while my management and colleagues appear understanding they say there's nothing they can do: in this company closed door means "don't bother me". My suggestion to put up a sign on the door wasn't acceptable.
They are not willing to flexibilize or making exceptions of a social convention to them even for medical reason - not at least for the new guy, who is also new in the industry. They don't want to make you an example for your colleagues. Imagine that after you everyone could want a closed door for 'X' acceptable reasons and they don't wanna loose control.
I suggested heavy duty earmuffs as an alternative but they all believe that would also signal that I don't want to talk to anyone. Their solution is to use normal headphones and listen to music.
You are backing off, proposing a solution, I have exposed your medical condition, you are suffering migraines, and they don't like it because it would "signal that I don't want to talk to anyone". Do you realize how disrespectful to your concerns it is? They know what's going on, what difference does it make what are you using in your ears? This is beyond ridiculous. This is again a clear signal that they are not willing backing off and expect you fit in what they consider acceptable, because they see you as a workforce, not as an individual.
which I also explained to my boss and HR
Yeah.. you talk to them, but on their mind it is your problem and should deal with that, not them.
This is my first job in industry and I'm very happy and wouldn't want to wreck it
They are counting on that to expect you flexibilize more and adopt one solution acceptable for them.
but I'm unable to find a solution that will satisfy everyone.
There's nothing much to do about it. Keep your clear conscience that you've been fair, reasonable and you've tried to make it work.
I don't want to sound pushy, and I don't want to sound like "it's my right to have a quiet environment". I'm looking for a fair compromise and way to bring up the issue again that won't make me seem unreasonable.
It is your right to have a positive environment for your productivity. They are sound pushy and unreasonable.
You see, I'm not advising you to impose your needs over the team's, wanna everybody to be quiet because of you - for example. That would be unreasonable. You've showed us you were being reasonable. They just won't change any of their social conventions and rules for the new guy. They don't want the new guy as a "bad" example.
Your situation is like this one in a job opportunity proposal:
HR - How much is your salary expectation?
Me - $100,000/year.
HR - We offer you 90.
Me - I would accept 95.
HR - We offer you 92.
Me - ¬¬
How can I make it clear that this isn't working for me?
Try a noise-cancelling headphone and do your best job while seeking for one place that matches with you.
Everybody will be happy - if your current company won't, they'll have learned a lesson then.