some med schools may accept you on the contingency that you are finishing your degree before matriculation. i would try to find 1 year MS programs but I doubt they exist for something like biochem. it would have to be non-thesis and you would probably have to pay with loans (no assistantships available).
looking around universities in my home state, i found a 1 year MS program in anatomy that looks interesting especially for a premed.
edit: it's not an MS but a "certificate" but it doesn't really matter.