Ouch. Unfortunately, whether a "problem" is or isn't any of those things, they're still situations that are being experienced. So no matter where "blame" (There should be no blame or shame, but our brains don't like that concept) falls, taking steps to allievate your troubles is the most important thing. Cause you deserve better than feeling bad about whatever a situation is and sitting in it.
Shoutout to my therapist who is still trying to make me feel that. Whether it is or isn't my fault, it is my problem. And I don't deserve to suffer in my problems just cause they exist. And there are steps I can take to minimize the effects of these problems in my life!
Can't brush your teeth properly? Keep a toothbrush in some water (or even better, antiseptic non alcoholic mouthwash!) Near where you sit. You don't have to spit or rinse or all that, but you're still breaking up the biofilm that does the most damage to your teeth! No actually needing to care about hygiene required. Maybe chew xylitol gums and get xylitol candies like Zollipops- they change your mouth PH to reduce bacterial growth (like the kind of bacteria that causes bad breath and cavities).
Can't work on your assignment at home? Congrats, now you're going straight from school to the library for an hour. Or you're making a corner of your bedroom SPECIFICALLY for working on things- that is no longer a part of your bedroom, but your office, and you're only allowed to enter that few square feet when you're ready to be productive. Or you're gonna ask your teacher to hold you to multiple littler deadlines, no excuses, so that you can get smaller-ish chunks of work done at school- maybe during lunch, maybe during study hall, maybe on the bus. Even if you are lazy, you've identified that being at home is what triggers that laziness, so you can avoid it.
Can't pick up on social cues? Doesn't matter whether it's the Autism or not, you have a record of not being able to. Even if you are clueless, cluelessness isn't a moral failure. It is what it is, and sucks to deal with. And if it was in your control you'd probably have already fixed it because the frustration is a constant (trust me, I know). So you've gotta live with it no matter the cause, and judging yourself for it makes it harder unnecessarily.
What if you don't need therapy and need to "toughen up"? Cool. If you were gonna be tough on your own, you would be. Therapy can be a tool to help you toughen up. It's like exercise, therapy appointments put a little stress on you over time so you build up the ability to handle it, rather than overloading on stress in the gym of sucky real life and injuring yourself- setting you back on your ability to handle it.
What if you need to work harder? Has making yourself work harder EVER worked out long term before? Probably not, just added more stress to you. Instead consider how you can work DIFFERENTLY. Work around your problems if you can't tackle them outright. If you can't fix your problem, work on mitigating the problems that those problems cause.
What if you can't fix it, and you have to learn how to deal with it? Well, congratulations, you've cracked the code then. Now your job is to figure out how to make it as easy as possible on yourself to live with it. BECAUSE YOU DO NOT DESERVE TO SUFFER NO MATTER WHO'S FAULT IT IS.