We report on a detailed study of the intensity dependent optical properties of individual GaN/AlN quantum disks (QDisks) embedded into GaN nanowires (NW). The structural and optical properties of the QDisks were probed by high spatial resolution cathodoluminescence (CL) in a scanning transmission electron microscope (STEM). By exciting the QDisks with a nanometric electron beam at currents spanning over three orders of magnitude, strong nonlinearities (energy shifts) in the light emission are observed. In particular, we find that the amount of energy shift depends on the emission rate and on the QDisk morphology (size, position along the NW and shell thickness). For thick QDisks (> 4 nm), the QDisk emission energy is observed to blueshift with the increase of the emission intensity. This is interpreted as a consequence of the increase of carriers density excited by the incident electron beam inside the QDisks, which screens the internal electric field and thus reduces the quantum confined Stark effect (QCSE) present in these QDisks. For thinner QDisks (< 3 nm), the blueshift is almost absent in agreement with the negligible QCSE at such sizes. For QDisks of intermediate sizes there exists a current threshold above which the energy shifts, marking the transition from unscreened to partially screened QCSE. From the threshold value we estimate the lifetime in the unscreened regime. These observations suggest that, counterintuitively, electrons of high energy can behave ultimately as single electron-hole pair generators. In addition, when we increase the current from 1 to 10 pA the light emission efficiency drops by more than one order of magnitude. This reduction of the emission efficiency is a manifestation of the "efficiency droop" as observed in nitride-based 2D light emitting diodes, a phenomenon tentatively attributed to the Auger effect.