Do I need to have taken physics in high school to major in bioengineering at a top tier university?

Physics is a required class for any science major. Not having a high school leve course in the subject is a huge red flag. The difference is in biochem you only have two classes (equivalent to two super intense AP classes, so a basic HS introduction is still expected) but anything involving engineering involves a lot more.
Basically you need to take a physics class.