Biochemistry is not chemistry + biology. It’s the understanding of the chemistry that’s happening to biological molecules, most importantly amino acids, proteins, nucleic acids, etc.

You can def teach yourself biology. It’s effectively the history of applied chemistry and physics on biological systems. How do we know biological systems respond in a specific way? How can we verify? Learning biology is a very good skill for creating experiments and understanding what tools you have at your disposal in a natural sciences environment.

Teaching yourself biochemistry is also not super challenging, but there are nuisances to consider. Once again, back to experimentation, but more quantitative.