This isn’t that uncommon a situation, not only in school but afterwards as well. Where you go to school or where you get the first job can have a lot to do with chance and not just your talents.
I’d recommend getting into the nearby program you like better, and plan on transferring to a better school later. Find out what credits will transfer and what won’t, so to spend less time re-taking classes.
Spend as much energy on design as you can, do the designboom.com competitions and take the design of artifacts class at cousera.com.
Consider this year a dry run, pushing yourself to achieve entrance to the best program you can, and use these lessons when it comes time to get into the job of your dreams once you finish up school.
And remember that design is a journey. where you fit best - where you do your best possible work may not be at a big name school or a famous consultancy. the capacity for great design is everywhere.