We investigate the effect of interactions in zero-dimensional polariton condensates. The shape of the condensate wave function is shown to be modified by repulsive interactions with the reservoir of uncondensed excitons. In large micropillar cavities, when uncondensed excitons are located at the center, the condensate is ejected toward the pillar edges. The same effect results in the generation of optical traps in wire cavities. Once polariton condensates are spatially separated from the excitonic reservoir, spectral signatures of polariton-polariton interactions within the condensate are evidenced.