We study theoretically two electron-hole pair states (biexcitons) in core/shell hetero-nanocrystals with type II alignment of energy states, which promotes spatial separation of electrons and holes. To describe Coulomb interactions in these structures, we apply first-order perturbation theory, in which we use an explicit form of the Coulomb-coupling operator that takes into account interface-polarization effects. This formalism is used to analyze the exciton-exciton interaction energy as a function of the core and shell sizes and their dielectric properties. Our analysis shows that the combined contributions from quantum and dielectric confinement can result in strong exciton-exciton repulsion with giant interaction energies on the order of 100 meV. Potential applications of strongly interacting biexciton states include such areas as lasing, nonlinear optics, and quantum information.