This is similar to the state of CS majors at some universities. Since the rising popularity of the CS major means that CS departments are full to overflowing at many schools, it may be very competitive to get into the CS major if one is not directly admitted as a frosh (e.g. UCSD, UIUC, Washington are common examples; http://talk.collegeconfidential.com/discussion/comment/19262574/#Comment_19262574 lists various schools).
Fortunately, CS (which the OP is interested in) at Michigan is not difficult to get into, according to https://www.lsa.umich.edu/students/academicsrequirements/majorsminors/electricalengineeringandcomputerscience/computerscienceengineeringdivisionofeecs/majorcomputerscience . The OP needs a 2.5 GPA with a C in each of four prerequisite courses. Whether that is acceptable to the OP’s parents is another story.