You can contact the Biology Department via email and explain your situation.
Turns out that sometimes, while a lab "appears" full, it is actually just locked to other students to prevent unnecessary switching. (Makes sense I guess because if there are 90 labs and a mass of students in about 30 of them, there may not be enough resources to conduct the assignments properly and accurately).
If you have an unresolvable conflict (i.e. No other way to fix the problem) and it seems you do, then they should assist you without too much mess