Your biggest issue will finding an undergrad program in aerospace/aeronautical engineering. There just aren’t that many colleges that offer it as a major at the undergrad level. (Aerospace/aeronautical engineering is primarily a graduate MS degree.) It generally recommended that if you want to have the option of doing aerospace/aeronautical engineering that you major in mechanical engineering. I have a number of friends and family members (including my dad) who worked in the aerospace industry and not a single one of them were aerospace majors. They majored in either mechanical or electrical engineering and were hired into the aerospace industry upon college graduation and later did grad work (paid for their employer) in aerospace/aeronautical engineering.
BME is another engineering field which is primarily a graduate field and many entry level jobs require a MS in BME for consideration. While an undergrad BME degree has more overlap with the pre-med requirements than do other engineering majors, a BS in BME doesn’t always mean good post-graduation employment prospects.
So–keep this in mind when considering potential majors.
If you’re sure you want to be an engineering major, then you do need to start out as engineering major freshman year since engineering has a quite rigid curricula and you need to take your intro math, science & engineering courses freshman year or risk needing extra time to graduate.
Also be aware that many people find it difficult to maintain the 3.7+ GPA needed for med school admission as an engineering major. (And no, med school adcomms will not cut any slack for having a “tough” undergrad major.)
If you want an undergrad degree field that offers more employment potential than bio or chem, consider physics or mathematics/statistics. Better employment options than bio or chem without the lock-step curriculum of engineering. And an undergrad math or physics degree mean you can switch into an engineering field for grad school with only some minor re-tooling. (D2 was a cognitive science and math double major undergrad. Her Plan B in case she didn’t get into med school was to get her MS in either BME or biostatistics–which is a really hot field right now with lots of employment options. D1 was a physics & math double major with a chem minor; her Plan B was a MS in BME or a PhD in health physics.)
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As for the aerospace and medicine combo–look up Randy Lovelace. He invented the first high altitude breathing apparatus for flight pesronnel and personally jumped out a plane at over 40,000 feet to prove it worked. He was also NASA’s first medical director and devised the testing protocols we still use to today to screen potential astronauts.
[William Randolph “Randy” Lovelace II](http://www.nmspacemuseum.org/halloffame/detail.php?id=19)