I hear something different from your RC. If you were on top of a nomination slate, they would have already reviewed and made a determination. You are not competitive enough on your nomination slate to be considered so they are not requesting a waiver. Remember, that is not really a National contest. You only compete on your nomination slates. It is very difficult for a normal high school student to make it off the NWL. 25-30% of each incoming class has some education past high school. If you were denied a waiver, then that would be a different discussion.
I would suggest that enlisting is the last option as
@WheeledMech states, you may be an enlisted soldier for a few years. You have a 4 year ROTC scholarship that you should be proud of. My advice would be to try ROTC and let the waiver process play out. If there is truly a mistake and you do not have the disqualifying conditions, ROTC will be able to work those things out as they have time. One of the ROOs would have to confirm, but I am pretty sure that if you have a four year scholarship, it will cover the entire first year even if the waiver doesn't come for a few months after the start of the academic year. The waiver authority is different for each nomination slate as well. If for some reason after your first year of college, you still want to enlist, then have at it and do not look back knowing your did everything you could to chase your dreams.
If your goal is to attend West Point, you will not be able to "hide" from whatever condition you have. Serving on Active Duty will not avoid the DoDMERB next time you apply. If you enlist, the earliest class you have a chance to apply to is 2024. You will have to go through the same medical review process in two years.
Also, applying from college as a re-applicant has fewer obstacles that may be outside of your control if you were enlisted.
I guess to answer your process question, enlisted soldiers compete for a service connected nomination and appointment. They work similar to MOC nominations but the mechanics are different. Your Army Chain of Command completes the endorsement which acts as the nomination. You then go through the same process competing for openings against others with the same nomination. Nominations or endorsements are unlimited, I think their are around 75 openings. The good news is that some of these do not get used each year as they seldom get that many qualified applicants.