I didn't know this when I was going through undergrad, but if your school separates biochemistry into two semesters (Biochemistry I/II), it's very likely you'll need both for the MCAT, which tests heavily on metabolic processes you won't learn until Biochemistry II, which is not generally a requirement for medical schools or most typical pre-med majors outside of the chemistry department. It's kind of like Organic III, you know there's more science to learn, you just assume your school only requires the relevant stuff. Not true.
That was a pearl-clutching realization for me in my last semester of college as I was preparing for the MCAT, and one that I think hurt me because by the time I found out, there was not enough room in my plan for the cycle without postponing a year, and I just wasn't willing to do that.
I could be wrong here but it sounds like you want to take Organic II and self-study Biochem I/II in parallel prior to your May test... which means that by the time you finish your spring semester in April, you will only have a few weeks' familiarity with major C/P and B/B content areas and will have been trying to bridge gaps in your understanding across several courses that build on each other.
I don't want to tell you to push back your test, because I'm an applicant and literally nobody to offer advice to anyone... but consider sitting down with someone that tutors biochemistry at your school and ask them how you might be able to do this intelligently, if you choose to press forward.
Seeing my process from the other side now, I can acknowledge I wasted a lot of time and effort into endless rabbit holes trying to study for the MCAT because I just didn't know what I didn't know. I assumed all coursework was modular and could be taken and processed in whatever order you want, and that was just not my actual experience.