This work presents a theoretical investigation of excitonic and biexcitonic states in cylindrical wurtzite III-nitride quantum dots, focusing on the influence of internal polarization fields and indium composition on their electronic and optical properties. The confinement potential is modeled using a bimodal Woods–Saxon profile that incorporates both band offsets and dielectric self-energy corrections, providing a realistic description of carrier confinement. Single-particle states are calculated using the finite element method, while exciton and biexciton complexes are analyzed through a variational Monte Carlo approach. The results reveal that the combined effects of piezoelectric polarization and spontaneous polarization significantly distort the confinement potential, leading to strong spatial separation of electron and hole wave functions and substantial modifications of exciton and biexciton binding energies. Increasing indium concentration three times enhances the internal electric field and leads to a clear redistribution of carrier density across the quantum dot. This effect reduces the electron–hole overlap and results in a decrease of both exciton and biexciton binding energies in larger quantum dots, while in smaller structures (heights below ∼2 nm) the confinement dominates, leading to an opposite trend and partial stabilization of biexciton states. The calculated exciton transition energy for a cylindrical quantum dot with 2 nm height and 10 nm radius is approximately 2.5 eV, in good agreement with reported experimental values (∼2.55 eV) for similar structures, confirming the validity of the model. In addition, the nonlinear optical response is analyzed using a three-level exciton–biexciton scheme. Biexciton transitions exhibit about two times stronger response than excitonic ones. Lower indium content induces a blue shift, while higher concentration reduces peak intensity due to enhanced carrier separation. These findings demonstrate how the interplay between internal polarization, composition, and quantum confinement governs excitonic complexes and nonlinear optical properties in III-nitride quantum dots.