A photoluminescence (PL) study of pseudomorphic modulation-doped AlxGa₁₋xAs/Iny Ga₁₋yAs/GaAs heterostructures possessing high electron density shows a fundamental change of the PL spectrum under excitation density increase. In its high energy tail the PL peak undergoes principal transformations caused by repelling the Fermi-edge singularity (FES) and excitonic states. The character of repelling depends crucially on the excitation density and temperature. At low temperatures an appearance of the FES feature has been observed for the first time under excitation density elevation. This appearance is accompanied by formation of an abrupt high energy edge and occurs far below by intensity the hybridized n = 2 exciton manifestation. Strong screening of the n = 2 exciton state by photoexcited carriers is observed. The PL behavior under excitation density increase and temperature elevation near the Fermi edge is explained in terms of strong carrier density effect on the FES manifestation and is referred to the two-dimensional (2D) electron gas properties not yet explored theoretically.