I would absolutely update the schools about your grades since it can only help you. You're saying you got a full-ride scholarship at one of the medical schools you have been accepted at, but there is another school you would rather go to pending them giving you matching tuition? I wouldn't mention any type of scholarship to the schools you are trying to get off the waitlist at. You are putting the carriage before the horse. Get off the waitlist, and then you can bring up the scholarship.
Overall, you should definitely go to the school which will be the cheapest. Overall, your success is based on YOUR study habits and effort, not the school you attend (for the most part).