A few random reflections, rather than a well-thought-out response to a question only you can answer:

> it's become unbearable
> hardly a single minute where I am able to concentrate

I'm amazed that anyone would be able to tolerate this for a 'few years' and not immediately jump at the chance to be relieved of it. Especially if it doesn't cost anything (I'm assuming you're an employee, so there is no extra financial burden to having your own office).

What is it you think you might regret? Loneliness and isolation? You've said that you enjoy being in the office for physical meetings, talk at the coffee machine, kitchen etc... sounds like with the solo office you would still have those benefits without the downsides of your current situation. Or is the perceived regret around some kind of social obligation to your coworker? Just off the top of my head, your suggestion that your conflict avoidance prevents you from telling him how you feel could also indicate that you subconsciously want to please him, to not 'rock the boat' in this relationship and so moving out of the shared office may feel like you are snubbing him or somehow breaking the unspoken social contract that is lurking in the back of your mind. I'm just hypothesising, I know almost nothing about you or the situation, however I can't help wondering if this is what underpins your reluctance to accept an offer which will very clearly relieve you of a situation that you have described as 'unbearable'.

The amateur psychologist in me wants to ask if there is perhaps some aspect of fear of failure, in the sense that right now you have an excuse for not producing your best work and there could be a possibility that once you move offices you will somehow be under the spotlight because, now you have the ideal working conditions, the pressure is on to be that mythical 10x developer who cranks out perfect code in record time. Nobody wants that pressure. As I said, I know nothing, just trying to throw out some suggestions about what is behind that reluctance or fear of regret.

About that cough: I'm not going to agree with you that you shouldn't discuss it, perhaps that conflict avoidance is something you want to challenge yourself about because it's a reasonable subject to bring up in a reasonable way... however speaking as someone who has also had a persistent cough for several months, believe me when I say it is just as deeply irritating for the person who is doing the coughing and more than likely they would absolutely like to stop if they could! However if your co-worker is as proud and independent-minded as me, then he probably does need someone to gently (or frustratedly) remind him that he probably really does need to see a doctor about it. I have someone in my life who keeps reminding me of that and it genuinely motivates me to get medical help by knowing that other people around me are also finding it deeply irritating. Your mileage may vary, as the saying goes.

One more tip, as I have been sharing an office for a while with someone who has quite a lot of noisy teleconferences: noise-cancelling headphones really are effective. I put myself off from trying them for a long time, because reviews always say that they are better for background noise rather than voices. This is true, the voices never perfectly disappear but they do become so incredibly quiet as to be easily ignored and with some fairly chilled focus-music I am truly amazed by how I can stay in the zone even with someone chattering away on speakerphone right next to me. Bose QuietComfort SE, absolutely did the job for me.