$100,000 in debt is too much for undergraduate, and you need a cosigner or parent loans (not a good idea for either you or your parents or cosigner).
The USMA is for those whose goal is to become an officer in the Army. If that is not what you want to do, then it is not suitable for you.
Looks like neither is really a good choice for you. Do you have any other (affordable) options?
If not, can you take a year off school (no college courses after high school graduation), work to save some money for school, and reapply to seek full ride merit scholarships or sufficient financial aid?
Examples (verify on school web sites and check for availability of your desired majors):
http://automaticfulltuition.yolasite.com/
http://competitivefulltuition.yolasite.com/