How much would Duke or Dartmouth cost? Consider whether you would rather apply that money to medical school.
https://www.aamc.org/download/152968/data/debtfactcard.pdf
Note that Dartmouth’s ABET-accredited engineering major (BE degree) commonly takes more than 12 quarters to complete, although do it without extra time. Dartmouth also offers a non-ABET-accredited BA degree program in engineering that does not require more than 12 quarters (Dartmouth is on the quarter system, so 12 quarters = 4 academic years).