Jet energy loss, photon production and photon-hadron correlations are studied together at high transverse momentum in relativistic heavy-ion collisions at RHIC energies. The modification of hard jets traversing a hot and dense nuclear medium is evaluated by consistently taking into account induced gluon radiation and elastic collisions. The production of high transverse momentum photons in Au+Au collisions at RHIC is calculated by incorporating a complete set of photon-production channels. Comparison with experimental photon production and photon-hadron correlation data is performed, using a (3+1)-dimensional relativistic hydrodynamic description of the thermalized medium created in these collisions. Our results demonstrate that the interaction between the hard jets and the soft medium is important for the study of photon production and of photon-hadron correlation at RHIC.