what kind of design??
I think Art institute is suppose to be a very good school....
Columbia College in Chicago
University of Columbia in New York
Art Institute of Chicago
Oberlin College
Carleton College...
If you want to combine your interest in art with some flexibility and good career prospects, you might want to consider a degree such as Interactive Media Design (half design, half computer programming...
What would be useful for you is some kind of work experience with people with mental health problems or learning disabilities.
You could try the nhs website and have a search see what is on off...