Congrats on the full ride to OSU, that’s great. What is your annual cost to attend Notre Dame?
You are correct, if you did not apply directly to Mendoza to begin with, then you will have to apply for transfer in the spring of your freshman year (to start fall of sophomore year). Just to make sure you know, all freshman start out in the First Year of Studies program, regardless of the college they applied to https://firstyear.nd.edu/academics/