You sound surprised that pre-requisites are required and just by having them completed you aren’t guaranteed admissions into competitive majors at competitive universities. As my snarkiness implies, they are required and you aren’t guaranteed admission by having them completed.
Any engineering, computer science, and economics majors are typically difficult to get into. Regardless, your GPA does need to come up … but do keep in mind that a major like chemical engineering often has one of the lengthiest lists of pre-reqs. Also, make sure this major actually lines up with what you want to do as a career. I’m not sure what exactly it entails at UCLA, but the UCB major is pretty much for people who want to work as chemists in a lab as a career.