Tough situation, and it's pretty much down to Monash having a massive growth in the size of new biomed enrolments without having the facilities to accommodate them. Given that they're providing a paid service for a degree consisting of core units, they absolutely should open up more places in the unit (I suspect that they did this for some second-year units this year because of the large second year cohort size + the significant number of third-years who needed to complete second-year subjects).
Best case scenario is that they open up more places in the Sem 2 units closer to the semester start date; I strongly doubt that you're the only person in this situation and I can't imagine that the Faculty is going to leave all of those people high-and-dry. I would advise that you maintain contact with the course coordinator (if memory serves it's Yvonne Hodgson) to 1. Talk about your problem and 2. Stay up to date with any decision the faculty makes regarding opening up more places.
Worst case scenario is that you're set back a year (because you'll need to wait a year to do these first year subjects). If I were in this scenario, I'd contact the FACULTY OF SCIENCE and enquire about a tailored course-plan whereby you would take 4 science units per semester. This might be helpful in the long-run for your BSc because you can get it over and done with sooner (you get credits and prerequisites done quicker than in a classical double degree scenario). This will keep you busy for however long you need until you can get your biomed units back into order. Don't forget that tha faculty of science is your managing faculty so they're responsible for helping you sort this out. (Note that this paragraph is under the assumption that you DONT get access to the biomed units in Sem 2, which I maintain is still rather unlikely that they'd leave people in that situation!).
Alternatively - and some people might prefer to do this - you take a semester or toe off and pick up your degree in Sem 2 of next year. This is super annoying academically-speaking, but it gives you the opportunity to work for a year and makes some money/travel a bit/volunteer somewhere/do whatever.
Keep in mind that my suggestions aren't comprehensive because I'm A) not affiliated with the university more than as a student and B) haven't been in this situation before, so I definitely don't understand it as well as the BSc course enquiry people (or indeed the staff at the faculty of MNHS). They should be your first and continuing point of call, because they're the ones who can until mutely rectify the situation in the best way for you.
Good luck, and let me know if you have any more questions!