Education Program Manager
As an architect who became an Interior Designer I can say that the transition was easier than it would have been if I were an Interior Designer trying to become an architect. So, my suggestion is that if you are in doubt, go to Architecture school and then you can do a Master or other courses to become an Interior Designer. Please notice that NCIDq (http://www.ncidqexam.org/exam/eligibility-requirements/) is the certification required in most states to practice as an Interior Design and they do accept an Architecture Degree but you must have more hours of experience working as an Interior Designer.
Another advantage of Architecture is that salaries are usually higher than in Interior Design. You can check the United States Bureau of Labor statistics for current salaries (http://www.bls.gov/)
I hope this helps and good luck!