Two-dimensional Ruddlesden-Popper hybrid lead halide perovskites have become a major topic in perovskite optoelectronics. Here, we aim to unravel the ultrafast dynamics governing the evolution of charge carriers and excitons in these materials. Using a combination of ultrabroadband time-resolved THz (TRTS) and fluorescence upconversion spectroscopies, we find that sequential carrier cooling and exciton formation best explain the observed dynamics, where exciton-exciton interactions play an important role in the form of Auger heating and biexciton formation. We show that the presence of a longer-lived population of carriers is due to these processes and not to a Mott transition. Therefore, excitons still dominate at laser excitation densities. We use kinetic modeling to compare the phenethylammonium and butylammonium organic cations while investigating the stability of the resulting films. In addition, we demonstrate the capability of using ultrabroadband TRTS to study excitons in large binding energy semiconductors through spectral analysis at room temperature.