You seem to put too much emphasis on unverified personality/behavioural tests. You mention Myers-Briggs. From Wikipedia Myers-Briggs - Criticism:

Many of the studies that endorse MBTI are methodologically weak or unscientific.

That's a nice way of saying Myers-Briggs is rubbish.

You also say:

Some tests even suggest slight Asperger, combined with what I suspect is a healthy dose of OCD.

A self-test can't diagnose Asperger's or OCD. Only a qualified mental health professional can do that. If you're really concerned about it, get it checked out. I have personality traits that some laypeople have thought was Asperger's and OCD. A mental health professional who I'd been seeing for a long time dismissed both out of hand. Having one or two traits doesn't mean you have the condition.

I don't understand what you mean by "introvert SE". Stack Exchange? South East? A search didn't find any English language results. I do understand the introverted side, so I'll ignore "SE" unless someone tells me what it means.

I am naturally introverted. I like people, but I'm often uncomfortable or awkward socialising. When programming I often use earbuds to play music I like. The music drowns out background noise of telephone calls and work conversations. Because I've listened to these tracks many, many times, I can tune them out. If you asked me to name the tracks I've listened to in the last fifteen minutes, I'd only be able to tell you the last one. I'm listening to music as I write this answer and I can't remember what was played before the current track.

You say:

I cannot blast music in my ears all day long, and even just having headphones on causes me to develop headache (they exercise pressure on the head)

You don't need to "blast" music, and doing so would damage your hearing. Play music at a comfortable level for you. Since the pressure of headphones applies pressure to your head, use earbuds or some other design that doesn't put pressure on your head. At home I have a lovely set of wireless headphones that sit very comfortably on my head without any noticeable pressure.

If people are talking loudly next to your desk about non-work related things and disturbing you, it's acceptable to politely let them know they're disturbing your work and ask them to move. Don't call them out for not working! You're not their boss, but you are responsible for managing your own work, and organising your work environment to maximise your productivity without negatively impacting others' productivity. Another possibility is that by talking near you, they're giving you an opportunity to participate in their conversation. If you never talk to them, eventually they will see you as unfriendly and shun you. It's OK to participate in their conversation as long as it doesn't go on too long and impact your work.

The remainder of your question is about the social aspect. Human beings are social animals. This is a fact, but it can be hard for introverted people like us to accept this in a work environment. Surely a work environment is all about the work? No, not entirely. Getting on with your peers is very important, and this takes emotional intelligence, social skills, or whatever else you'd like to call it. You don't need to be as chatty as the chattiest person in the office, but you do need to raise your sociability to a minimum acceptable level. Ignoring the social aspect in favour of working 100% of the time would be like ignoring logic and program flow in favour of typing at a high rate of words per minute. Work on your weaknesses until they no longer trip you up. You don't have to become an expert, just as long as it's not holding you back.

As for "being more visible", be proud of your successes! Boast about your victories a little! "I'm so happy about the way that last project went! Sally asked me for a way to do X and I think this is a really neat way of doing it. Sally just loves it!" It sounds like this is what your boss wants. Your work reputation is all about what other people think of you and not at all about your productivity. You can argue that this is wrong and that it shouldn't be like that, and I'd probably agree with you. The reality is that looking valuable is more important than providing value to your company. That's not to say they're mutually exclusive. The best way to look valuable is to constantly point out recent things you've done that benefit the company and your team. Lying is also a very successful method that I've seen other people use, but I don't recommend it because some people always know the truth and are resentful of the liar getting ahead without merit. I'm sure your boss would be happier with an employee who everyone likes and gets their work done, than an unlikable employee who gets their work done.

In summary: