Why MET BioE at UCB and chemistry at Harvard if you want to study chemical engineering?
Meaning that your parents can afford up to $320k for your undergraduate costs?
These are generally considered reaches for all, unless you have some inside information (e.g. well connected prep school counselors) who can tell you otherwise.
What are the colleges you consider matches, likelies, and safeties? A fairly large number of Ohio public universities have ABET-accredited chemical engineering majors: https://amspub.abet.org/aps/category-search?disciplines=13&countries=US&states=OH