ChemEngMD, I know you are trying to help me and I truly respect that. I apologize if I sound like I totally disagree with because you make valid points. I know it's not the easiest route but did you switch out of your cheme major or you stuck with it?
You're falling into the same trap a lot of undergrad. freshman do. You're putting Chem. E up on this pedestal, and saying nothing else would be worth it (and not considering the VAST array of potential majors). You are also failing to consider that a large number of people apply multiple times, and not everyone is a 22 year old (although I was) in M1.
Assuming you make it into medical school, your chem. E degree will be nearly useless. The skills required, background knowledge and methods of learning are mostly different.
Most of my undergrad. friends were chem es, and several of my family members are chem. es. If you genuinely love math, you should consider statistics, computer science, comp. sci engineering, straight math, physics, etc. If you can really hack it in Chem E, chances are you can make it into med. school. So the whole "fall back plan" is kindof irrelevant.
All of the computer sciences and statistics have excellent job prospects (statistics often needs a masters, but the job market is pretty damn good for masters degree).
In short, take a serious look at the path you choose before you blunder your way into it.
And if you do end up doing chemical engineering....welcome to the island of misfit toys, you'll fit right in here!