We study the excitonic structure of CdSe/ZnSe self assembled quantum dots (SAQD) by magneto-photoluminescence (PL) spectroscopy. Using fixed 200 nm apertures through a metal film, we are able to probe single narrow (200 micro-eV) spectroscopic lines emitted from CdSe quantum dots at 2K. Using linear polarization analysis of these lines, we find that approximately half of the quantum dots are elliptically elongated along the  direction. The other half of the QDs are symmetric, with emission lines which are completely unpolarized at zero field and exhibit no doublet structure. Using an applied magnetic field, we obtain the diamagnetic shift and the g-factor for several symmetric dots and find that the variation from dot to dot is random, with no systematic dependence with emission energy. In addition, we find no correlation between the diamagnetic shift and the g-factor.