Don't go yet. See if the art school will let you defer enrollment for a semester or a year. It sounds like you have very serious doubts and need a very substantial break. Burnout is not something, in my experience (though I am not an artist), to take lightly. A semester's or a year's break before enrolling in art school will give you a chance to do something different with your time, be with your boyfriend, and think deeply about what it would be like to go. It doesn't mean you would be turning your back on your ambition or your talent. It would mean acknowledging that there are other, equally important, priorities in your life besides your art education.
I took a break during my own education, partly because of burnout and partly because of a serious boyfriend who lived across the country, and it was one of the best things I ever did. It energized me and inspired me when I got back to school, and strengthened our relationship to be able to survive two more years of long distance (we are now engaged).
If your school will not let you defer, talk with someone you trust in the admissions department. Explain your situation (the burnout) and ask for his/her honest opinion of your chances of getting admitted a second time if you decide not to go this year and apply again for next year. Be sure to emphasize that their school is the right place for you, etc, but you are worried this is the wrong time, and by going now you might compromise your potential. The worst they can say is that you wouldn't get in again, in which case you might decide to go now, but at least you will have explored all your options.
Lastly, a slight tangent...I know that in some European countries taking a "year off" between high school and college is mandatory. People can choose between all kinds of community service jobs and projects to do during their year off, and then go to college with one year more of perspective, experience, and maturity, not to mention a long break from studying and academics. I always thought this was a brilliant system. Of course it may not be perfect for everyone, but if your gut is telling you to take a break, I would not ignore it.