Symmetry of photoexcited states with two photoinduced carriers in two-dimensional Mott insulators is examined by applying the numerically exact diagonalization method to finite-size clusters of a half-filled Hubbard model in the strong-coupling limit. The symmetry of minimum-energy bound state is found to be s-wave, which is different from a d_{x^2-y^2} wave of a two-hole pair in doped Mott insulators. We demonstrate that the difference is originated from an exchange of fermions due to the motion of a doubly occupied site. Correspondingly large-shift Raman scattering across the Mott gap exhibits a minimum-energy excitation in the A1 (s-wave) channel. We discuss implications of the results for the Raman scattering and other optical experiments.