Colloidal quantum dots (QDs) have attracted interest as materials for opto-electronic applications, wherein their efficient energy use requires the understanding of carrier relaxation. In QDs capped by bifunctional thiols, used to attach the QDs to a surface, the relaxation is complicated by carrier traps. Using 2D spectroscopy at 77 K, we follow excitations in thiol-capped CdSe QDs with state specificity and high time resolution. We unambiguously identify the lowest state as an optically allowed hole trap, and identify an electron trap with excited-state absorption. The presence of traps changes the initial dynamics entirely by offering a different relaxation channel. 2D electronic spectroscopy enables us to pinpoint correlations between states and to easily separate relaxation from different starting states. We observe the direct rapid trapping of 1S_3/2, 2S_3/2, and 1S_1/2 holes, and several competing electron relaxation processes from the 1P_e state.