my DS1, recently turned 6, is exactly like this when it comes to background sounds, and has always preferred to work privately when he was younger. Still does sometimes. I don't think the privacy part is an issue unless it's part of perfectionism getting in the way.
Auditory processing - DS1's OT first brought it to my attention. I did not realise beforehand that it was something unusual. As he got older, he told me he simply could not think when there are others chattering around him. His OT did a bit of sound therapy with him (some strange filtered music), and I did notice that he would be calmer and more together for the rest of the day.
Right now we are focused on his vision processing issue and he is under the care of a vision therapist (finally found one!!). I recently read on the Eides' website on 2E issues that many children with vision issues tend to also have auditory processing issues. Their theory is that because the vision is compromised, the auditory becomes hypersensitive to compensate. (Note: I'm not suggesting that any of your children have vision problems, just sharing something that might or might not be useful for auditory processing.) This really put everything together for me. It took us a very long time to realise the full extent of his vision issues (almost a year and a half), and it's only just recently that I'm understanding how it has affected his gross motor skills, reading, AND auditory processing.
Reading The Mislabelled Child, I was taken aback to learn that children with vision processing issues can have trouble reading others' facial expressions and thus miss social cues - I finally realise why DS1 always go by the tone of my voice rather than the expression on my face and seemed to have to ask the obvious. It's because he can't trust his senses to give him correct information.