According to the website, it states you cannot switch into BME unless you are direct admit. I would contact UCSD BME advising to see if it possible to switch.
https://students.ucsd.edu/academics/advising/majors-minors/capped-majors.html
Freshman Student Advising
(3.2.1) Q: Can I still apply for Bioengineering or Bioengineering: Biotechnology majors if I was admitted to UCSD with a different major?
A: No, The only way for a student to become a Bioengineering or Bioengineering: Biotechnology major as a freshman at UCSD is to be directly admitted from high school at the time of entrance into UCSD. (Margene Wight, 2007.06.11)
(3.2.2) Q: What is the minimum GPA necessary to get into the Bioengineering: Premedical major from the Pre-Bioengineering: Premedical status?
A: Pre-Bioengineering: Premedical majors who have achieved a GPA of 3.0 or better in the eight required pre-major courses (Mathematics 20A-B-C; Physics 2A-B; Chemistry 6A; MAE 9 or 10, and one other pre-bioengineering course by the end of the freshman year) are assured of admission into the Bioengineering: Premedical major. (Margene Wight, 2007.06.11)