The effect of Coulomb interaction on exciton-polariton condensates in GaAs pillar microcavities with lateral size of the order of 10 μm has been investigated by means of a nonresonant excitation with various spot sizes. A local excitation with a small laser spot has been shown to allow for control of the spatial potential of the lower polariton branch in the pillar and manipulation of the polariton condensate wave function, polarization, and energy. Contributions to the blueshift of the condensate mode resulting from interactions within the condensate and from those of condensed polaritons with the photoexcited exciton reservoir have been separated, and the constant of polariton-polariton interaction in the condensate has been evaluated experimentally and compared with the results of the theoretical model.