Sounds like you have to learn how to say, "No, sorry, I can't do that now. Ask me again in 6 months." There will always be something in the future. If it's not exactly what is there now, it will be different. That's OK. No sense in wearing yourself out resulting in not having a future. Enjoy living now. Live to learn, live to enjoy, live to live. DON'T LIVE TO WORK and wear yourself out. Been there, done that. It's NOT worth it.
As for your brain never shutting down, although that doesn't happen to me, it does happen to someone I love and it certainly is debilitating. Just once, I managed to get him into a situation where he was actually, admittedly <gasp> bored. It did him soooo much good. We went out of town, rural location, and then as it worked out, everyone except he left the campsite and I somehow had his cell phone. He had no vehicle, no phone, no tablet, nothing to read, no bush to walk in, no stores nearby, no other people really. And he was like this for about 6 hours. It took him about 3 hours to get to boredom and the remaining 3 hours were like an entire weekend of holiday for him. Amazing.
Maybe try Yoga? Give up something that you are doing for someone else or give up something that can wait. Yes, there IS something that you can give up. Replace it with something for your wellness. Not just something you enjoy, but something to benefit your soul. And something that doesn't have firm obligations. So, if you feel crappy one day and don't want to go, it's perfectly okay to stay at home and eat ice cream on the couch for those one or two hours instead. Regardless of if you go or not, the time is still 100% only for you. No chores, no calls, no research, nothing. Pick flowers or something.
And, I'm slapping your wrist right now. NEVER FEEL BAD ABOUT WHAT YOUR PARENTS DO FOR YOU. Feel awesome that they are finding ways to help and that they have the resources to do it, plus the willpower to continue to search for solutions. It is NO ONE'S FAULT that you are who you are. It just is. I hear that you love, respect and are grateful for what your parents do. Your parents love you too and I'm sure that they don't for one minute complain that if it wasn't for you they wouldn't be in this mess. I have two children and both have or have had various long term issues that have depleted funds, depleted emotions, or depleted my sanity. I am a very selfish person. Yet it has never, ever crossed my mind (before today) to even possibly think that, "Well, if only he didn't have this problem, my life would be easier." It never occurred to me at all that a parent could possibly think that. From what you have said about your parents, I'm confident that they are on the same thought-train.
As for peers of your age-group: I can't see you spending much time at all with the average teen girl or guy. You are indeed old in many ways. Most teens won't have any concept of your life. That's okay. They can do their teen thing now. Then they'll have to grow up all of a sudden one day. At which point, you will be an official, independent adult, and you can revert to teenhood! LOL