We use the intense, 5-ns-long, excitation pulses provided by the fourth harmonic of a neodymium-doped yttrium aluminum garnet (Nd:YAG) laser to induce a strong high-energy shift of the photoluminescence of a 7.8-nm-wide GaN/Al0.15Ga0.85N single quantum well. We follow the complex relaxation dynamics of the energy and of the intensity of this emission, by using a time-resolved photoluminescence setup. We obtain excellent agreement between our experimental results and those of our finite-element modeling of the time-dependent energy and oscillator strength. The model, based on a self-consistent solution of the Schrödinger and Poisson equations, accounts for the three important sources of energy shifts: (1) the screening of the electric field present along the growth axis of the well, by accumulation of electron-hole dipoles, (2) the band-gap renormalization induced by many-body interactions, and (3) the filling of the conduction and valence bands.