Lead halide perovskites have emerged as platforms for exciton-polaritonic studies at room temperature, thanks to their excellent photoluminescence efficiency and synthetic versatility. In this work, we find proof of strong exciton-photon coupling in cavities formed by the layered crystals themselves, a phenomenon known as the self-hybridization effect. We use multilayers of high-quality Ruddlesden-Popper perovskites in their 2D crystalline form, benefiting from their quantum-well excitonic resonances and the strong Fabry-Pérot cavity modes resulting from the total internal reflection at their smooth surfaces. Optical spectroscopy reveals bending of the cavity modes typical for exciton-polariton formation, and absorption and photoluminescence spectroscopy shows splitting of the excitonic resonance and thickness-dependent peak positions. Strikingly, local optical excitation with energy below the excitonic resonance of the flakes in photoluminescence measurements unveils the coupling of light to in-plane polaritonic modes with directed propagation. These exciton-polaritons exhibit high coupling efficiencies and extremely low loss propagation mechanisms, which are confirmed by finite difference time domain simulations. Thus, we prove that mesoscopic 2D Ruddlesden-Popper perovskite flakes represent an effective but simple system to study the rich physics of exciton-polaritons at room temperature.