I'm a sophomore in high school and have been planning on majoring in chemical engineering after high school. My eventual goal is a Phd in Biochemistry. I hope to eventually do my own research in treating chronic illnesses. Would it make more sense to start with a general biology major and work my way up? If so would I be able to secure a moderate paying job so I can support myself and earn higher degrees at the same time?

I can tell you what worked for me. While earning a teaching degree, I worked with children in as many ways as I could. That definitely helped me in my teaching career. I morphed into library work and dealing heavily with the public. That caused me to pursue a grad degree in counseling psychology which I used in Libraryland as well as in a counseling setting.

So yes, work while you earn your degrees, but do work that is meaningful for those degrees. Not only with you get hands-on experience, but you will be earning money to apply toward tuition and books and housing.

It sounds like you have some challenging but fun years ahead of you!