This paper examines the unsteady propagation of a strong spherical shock wave in a non-ideal self-gravitating gas subjected to monochromatic radiation and an axial magnetic field. The flow is modeled under spherical symmetry, leading to a coupled system of nonlinear partial differential equations governing mass conservation, momentum balance, magnetic field evolution, internal energy, radiation transport, and self-gravitation. The Rankine-Hugoniot conditions are employed to describe the behavior of the flow variables across the shock front. To obtain analytical insight into the problem, the Lie group method is used to identify similarity transformations that reduce the governing system to a set of ordinary differential equations. These similarity equations are solved numerically using the classical fourth-order Runge-Kutta method. In addition, Physics Informed Neural Networks are implemented to compute approximate solutions by embedding the governing equations and boundary conditions into the learning framework. A comparative study between the Runge-Kutta solutions and the PINN-based solutions is carried out to evaluate the accuracy and consistency of the neural network approach. The results indicate close agreement between the two methods, demonstrating that PINNs can serve as an effective computational tool for nonlinear shock-driven flows. The study provides a unified framework combining symmetry-based analysis and physics-informed learning for the investigation of complex radiating and self-gravitating gas dynamic systems.