So I don't want to be accused of "profiling" students or your daughter, but she sounds very much like a typical engineering student. I can't speak fully to her shyness or what you describe as her lack of ambition, because I don't have more context, however I don't believe your daughter has to "overcome" her shyness. Unless it is dysfunctional in nature, or prohibits her from living her life normally (again, I don't know), I suspect if she finds the right school, and right major, her confidence may grow more naturally. College can be a very organic confidence builder, particularly as kids find themselves with those more like them in academic pursuits and interests. It gets easier for them to be the "real me." They find their niche, their crowd, and begin to develop a richer persona. Mt feeling is that It can still look quiet, and shy. Again shyness should only be an issue if it's painful for her, or problematic. Plenty of people live very full lives as shy individuals, and yet still find a way to advocate for themselves and engage in rich social experiences and careers.
I'm reminded of Supreme Court Justice Ruth Bader Ginsburg who currently serves on the Supreme Court.. Justice Ginsburg is so shy and soft-spoken that when she voices her opinion, the whole world strains to hear her words. Translation: when she speaks, everyone listens. Loud people are often tuned out. Shy people may be more effective in getting their message across (depending on the situation.)
I want to add that your daughter's academic interests/strengths are not very outward-focused - and require heavy brain crunch power. I'm thinking she is very intelligent, and suspect that her being introverted relates somewhat to how busy her brain must be doing all those mental cartwheels with applied mathematics. It's not a bad idea to enroll her in a public speaking class - if she agrees - but in my experience even considering something like this can bring on more social anxiety. But it's worth a shot to see if she will consider a class or program that is outward focused with social engagement built in.
As for the lack of drive, she has it in her somewhere. You can't'get those kinds of grades and even scores without some interest in doing well. She has to be staying on top of her homework and prepping for school exams. It may be she just needs an interest to fire her up.
That leads me back to her college major. I agree with Eric Ngyuen. Georgia Tech would be a terrific fit and you can't beat the low cost of tuition as a GA resident. Her interests in related medical subjects: neurology and radiology, make me think she is ideally suited for a major in bio medical engineering. You and she may not be aware that it's engineers who have "invented" our current X-ray technology, CAT scans and MRI's. This major also requires someone who can handle the highest level of mathematics. That's your daughter. It embodies all of her interests as you listed them in your question.
Beyond Georgia Tech other top engineering schools can be found at UPenn, Cornell, UMich, Purdue, GW, Cal Tech, Virginia Poly-Tech, USC, Carnegie Mellon, Penn State, UT-Austin, Duke, Rice, Case Western, Vanderbilt, UDel, and Drexel to name a handful. This list is by no means comprehensive but gives you a quick study of some of the best. A note of warning: bio med engineering is now one of the hottest majors. Some of these schools have limited spots. You'll need to do your homework on this to be competitive. Also, engineering majors carry a bigger course-load than their college peers. Some of these programs are set up for a student to graduate in five years, (Georgia Tech), others operate on warp speed and students graduate in four, (UPenn). The range reflects a range of philosophy in education - the five year program may place a heavier emphasis on students getting a more comprehensive exposure to liberal arts classes. Either way, at the end of the four or five years of college, engineers graduate as certified professionals. That professional affiliation and identity may also go a long way to helping your daughter with her sense of self in the world - in a good way.
Best of luck!