We report a photoluminescence study of excitons localized by interface fluctuations in a narrow GaAs/AlGaAs quantum well. This type of structure provides a valuable system for the optical study of quantum dots. By reducing the area of the sample studied down to the optical near-field regime, only a few dots are probed. With resonant excitation we measure the excited-state spectra of single quantum dots. Many of the spectral lines are linearly polarized with a fine structure splitting of 20\char21{}50 \ensuremath{\mu}eV. These optical properties are consistent with the characteristic asymmetry of the interface fluctuations.