It’ll probably depend on the school. I know that some schools do offer single rooms for certain mental health conditions, though rarely. You’d most likely have to obtain a doctor’s recommendation for you to live alone.
It’s probably out of the question. Pretty much all first-year dorms have some sort of communal/shared bathroom, and if they do have a kitchen, it’s communal. The only dorms that do have private bathrooms and kitchens are likely reserved for upperclassmen but are still shared between 2-3 students.
Don’t start your college search with dorms, though. Find colleges that you’re interested in and then have your parents or yourself inquire about possible accommodations.