Lawrence, Bard and Ithaca also have double degrees- and many others.
You might want to take a broader view of possible paths. This might relieve stress and help you continue to enjoy music. (And competitions are focused on the short term goal of winning. Think about whether time spent on technique for long term goals would be better.)
So your options are BM, BA in music or something else (CS would be a BS), double major, major/minor, or a non-music major while continuing violin on the side with private instructor and performance in extracurriculars or off campus (many talented students do this).
Read this carefully: http://www.peabody.jhu.edu/conservatory/admissions/tips/doubledegree.html
You may or may not want to audition. You can have good choices without an audition if that is what you choose. This forum has threads on liberal arts schools good for music. Tufts, Vassar, St. Olaf and College of Wooster come up. Many more.
Oberlin has a Musical Arts degree for musicians who want to get a BA. Look at websites for schools and see what programs each school has. Be aware that sometimes doing a BA in music, or doing a BA in something else but wanting to study violin, can actually be harder at a conservatory school with a lot of BM students.
Whether you choose BM or BA or BS, there are many many options. And if you feel behind, some schools let you enter as a BA and then transfer to the conservatory BM as you progress.
You will have to do research! But think about your path in very general terms, I think, before getting so specific 