Equilibrium Bose-Einstein condensation of exciton polaritons demonstrated in long-lived microcavities [Phys. Rev. Lett. 118, 016602 (2017)], proved that a driven dissipative system can undergo a thermodynamic phase transition at the limit where the quasiparticle lifetime exceeds the thermalization time. Here we identify the role of dimensional and polariton interactions in determining the degree of thermalization of optically generated traps. To distinguish the effects of trapping from interactions and lifetimes, we measured the polariton distribution under four non-resonant Gaussian pumps in a square geometry and compared it with the polariton distribution measured at each pump separately. We find that a significant redistribution of polaritons is caused by trapping and changing the density of states. Surprisingly efficient polariton-polariton scattering below the condensation threshold is evidenced by the depletion of the inflection point polariton. Our work provides a deeper understanding of polariton distributions and their interactions under various shapes of optically generated potentials.