I largely agree with the previous poster. You need to determine what you really want. Do you want to be an engineer who might want to consider med school or someone who wants to optimize their opportunity to get into med school.
Purdue’s engineering program is not for the faint of heart, especially their ME program. Their second semester ME Thermodynamics class is considered one of the hardest courses in the nation. I believe the average is something like a C.
http://www.huffingtonpost.com/2011/03/29/the-hardest-college-class_n_841930.html
I wouldn’t consider double majoring. The two majors would both consume too many hours even assuming some courses would be considered for both majors. If you are primarily interested in engineering and want to keep med school options open then consider Chem E. It will cover the Chemistry and Physics you need. You will still need biology, anatomy and physiology, nutrition, psychology and some more I have forgotten. All in all not very forgiving electives. If you have a lot of AP credits it may make it easier to finish in 4 years. If your attitude is that if your grades are good (3.5 or better) then go ahead and take the MCATs and see where it takes you. If you struggle then you have a shot as an engineer.
If your primary goal is to become a doctor then you may reconsider your priorities. There is not really going to be an easy engineering school although there are those you will be more likely to be at the top of their class. You can essentially major in anything to apply to med school so long as you have completed their prerequisite courses. Med schools consider GPA, and MCAT scores more than which school you attend.
I’m not trying to talk you out of it because it is doable. @mom2collegekids has a son who graduated as a Chem E and went onto med school. I don’t believe he double majored however.