How can I find the voltage across individual capacitors in a circuit?
I'm not entirely sure what you mean by conservation of current, but Kirchoff's current law certain applies here, as does Kirchoff's voltage law.

You're doing "steady-state" AC analysis, so start by computing the complex impedance of each capacitor at 300Hz. Then solve the circuit using your favorite circuit network methods with these constant impedances (nodal analysis, mesh analysis, etc.).