The interaction between magnons and photons has significant implications for quantum information processing and in spintronics. In an electromagnetic cavity, wherein photons are confined, the photon-magnon coupling can be enhanced and controlled more effectively. In this thesis, we investigate a model system wherein the interaction between an antiferromagnetic domain wall and cavity photons occurs via the inverse Faraday effect, resulting in a coupling analogous to optomechanical coupling. The coupled dynamics leads to the emergence of level attraction, a term used to describe the coalescence of two distinct eigenmodes in a region bounded by exceptional points. We reveal the impact of the Dzyaloshinskii-Moriya Interaction (DMI) on the coupled dynamics of domain walls to cavity photons. We demonstrate that the presence of DMI can affect the coupling between magnons and photons, depending on the geometry of the system. This finding has potential applications in the control and detection of DMI in antiferromagnetic materials. Using a different formalism, we provide a demonstration that the phenomenon of level attraction can arise in systems characterized by instability under non-equilibrium conditions. A formalism for characterizing the linear response of driven magnonic systems has been developed and we show that results can be reproduced using numerical micromagnetics. The developed theory facilitates the study of cavity magnonics using numerical micromagnetics.