Art history is a valuable in itself. You can go on to grad school in art history or other subjects,or enter any professional school, including medical, law, business, nursing etc. (with prerequisites).
You can get a PhD and teach (though positions are fewer than years past). You can study museum studies (see Harvard Extension). You can work for historical organizations. Teach high school.
You can work at many different types of jobs and are not limited to jobs in the area of art/art history.
During school you can do internships, volunteer and work to clarify career goals. But your career does not have to match your major.
I understand the financial worries and desire for a certain path, but I sincerely believe you can study what you most want to study- whether design or art history- and find a satisfying career path afterward, without deciding on career prematurely. It may be scary but you really can take the time to explore and figure things out.