Public Health is a capped major so you would need to finish the required pre-req courses with a minimum GPA to switch into the major.
http://bsph.ucsd.edu/new_students_major.html
There is no such thing as a “pre-med” major. You need to take the Medical school course requirements to apply, but you can major in anything you want.
Visit the campus, talk to students and find out for yourself if UCSD is right for you.