If you have headaches that have no clear cause then I sympathize because that is besides painful, probably very annoying and frustrating and can get in the way of a lot of things, making you function below your natural level.
I know people who had had terrible headaches, and they went away at some point. And they don't have psychological problems, as far as I am aware of.

Don't feel psychologically broken because you have headaches and once had a concussion. Yes, they can be connected, but in your case don't know that they are. And even if it is true, you can still function. There's people with only one hemisphere/half a brain, and no one suspected that because they are able to act normally.
There is no reason to believe something is physically wrong with your brain that causes all these problems and frustrations you now have and will make it impossible to move forward in life.

I sometimes fantasized that I had a tumor and that they would discover it one day, remove it, and my whole personality would chance. That all the things that I self-limit, self-sabotage, restrict myself in, or for some reason I can't explain don't work out, would suddenly automatically proceed. And that all my special talent, and the thing that makes me feel me, would also be gone.
But that's just fantasy.

You keep focusing on what you cannot do. Even when they are unimportant. No one that has the potential to be a friend will care if you are a poor driver, or that you have odd gestures.
People will react badly if you throw temper tantrums or act needlessly defensive. So you aren't all wrong. But the point is, you list things about yourself, but you list only negative things. There are positive things. You know them better than anyone.
And if you do have friends and are a poor driver, at some point they will make fun of it because to them it is not a big deal. And you should be able to handle it and know they will still be your friend.

Your life has the potential to change a lot in a few years, and likely it will. For good or for bad. A tiny event today can make your life be completely different in 10 years. Yes, it is scary. But it is also an opportunity. How many years did you lose? One? Two? That's nothing. Or you only lost 6 months, not really sure.
I lost more than a decade. And I have to go on. I lost 1/3rd of my life, 80% of my adult life so far. And I still have to salvage my life. I could be a professor running my own lab, have a wife and children, and have a 1 in 10,000 chance to win a Nobel Prize in physics. Yet I am a bachelor student who has a 1 in 20 odds of getting tenure at age 55-60.

If you think you have brain damage that will prevent yourself from passing the math test, you will probably fail again.

I failed basic algebra in the lowest level of high school. I aced multivariate calculus in university. I cannot explain the difference in my ability then and my ability now. By all accounts, my brain should be much poorer at learning new abstract things. But if I had to try to explain it, I would point to a "can-do vs cannot-do" mentality. If you think you are stupid, cannot possibly do math, I believe you self-block yourself. I guess it is a viscous cycle and I don't know tricks to break it. What I did is quit for years, forget how bad I was, then relearn everything myself, then ace the tests. That's not an option for you, I guess.
Second thing is sitting down and practicing over and over. I used to make terrible mistakes when writing one equation going to the next one. I understood the problem, but I would always switch around a plus or minus sign, copy an equation wrongly, and I would get the wrong answer. In fact, in a single problem I would make two copying mistakes, and an algebra mistake, while I was unsure if I was solving the problem correctly. Then I checked the answer and it was completely different and I wasn't even sure what I was doing wrong, or why.
I remember having a notebook and doing the same problem 20 times, getting stuck at the same point several times.

In fact, I still did that in uni for tests I aced. We would learn new methods to solve problems. I wouldn't do the exercises, or not enough of them. And then when practicing for the exam, I wouldn't be able to solve something simple and I had to do it 10 times. So 10 times 4 pages of equations to fix something I should already be able to do.
But it does help me ace tests. I can get the abstract idea, but I need to practice crazy amounts to not fumble on writing through problems.
If I don't do it and get lazy, I lose points.

I have to sit down hours and do problems I already did in the past, just to make sure I don't lose math ability. It is frustrating. I know for sure there are others who just learn it once, never have any troubles, go party, and pass the test.
But I can ace it, if I try hard enough.

I see you tried tutors and it is a basic algebra test. I cannot help you with details.

I did go to a psychologist. She said it sounded like 'giftedness with streaks of autism'. Now I believe a psychologist has no idea what they are doing. They make it up as they go along. Yet I wanted to tell my story and I wanted to have someone who would make sure I wouldn't weave myself into bizarre thoughts. I brood and ponder a lot. A lot. I always do it. Every night for 1 hour before I get to sleep. Always when I do endurance exercise. I am alone a lot. I always think, worry.

Sometimes I feel like a superhero, in my own fantasy world. In fact, I have my own fantasy world where I am a hero, or maybe rather a tragic anti-hero. Sometimes, I feel crazy and broken. I know I must be somewhere in between, regardless of how I feel. The way I worry/brood/ponder probably determines how I feel at that point. It is kind of like there are two 'me's', one that lives in the internal world, one that lives in the external. One that is who I think I am. One who is what others think I am. To me it is clear those are two very different personalities.

Anyway, I am digressing.