Both osteopathic (DO) schools and allopathic (MD) schools have physical exam courses which require students to practice on each other; osteopathic schools have OMM lab which is much more extensive, however. At most schools, people wear shorts and t-shirts, and only take their shirts off when they're actually working on the chest, back, etc, etc. Girls usually wear sports-bras, and obviously don't have to take those off. Most schools are very respectful of the students and their issues with their bodies; there's usually a disclaimer in the course packet that makes a big deal about modesty and maturity, responsibility and all that. Additionally, some schools put girls together in pairs and guys together in pairs. Some schools don't. Choose a partner who you're comfortable with, guy or girl; I think that's the most important thing.
You're learning medicine; the hangups people have with their bodies fade away pretty quickly when everyone realizes that they're all there to learn how to heal people, not be stupid and childish.
p.s. If you have concerns for religious reasons, talk to the administration to see what kind of accomodations they can make. It would be pretty awful if they made Muslim women sit in the OMM lab at one of the 50 tables with nothing but a sports-bra on.