Integrated photonics is poised to become a mainstream solution for high-speed data communications and sensing in harsh radiation environments, such as outer space, high-energy physics facilities, nuclear power plants, and test fusion reactors. Understanding the impact of radiation damage in optical materials and devices is thus a prerequisite to building radiation-hard photonic systems for these applications. In this paper, we report real-time, in situ analysis of radiation damage in integrated photonic devices. The devices, integrated with an optical fiber array package and a baseline-correction temperature sensor, can be remotely interrogated while exposed to ionizing radiation over a long period without compromising their structural and optical integrity. We also introduce a method to deconvolve the radiation damage responses from different constituent materials in a device. The approach was implemented to quantify gamma radiation damage and post-radiation relaxation behavior of ${\mathrm{SiO}}_2$-cladded SiC photonic devices. Our findings suggest that densification induced by Compton scattering displacement defects is the primary mechanism for the observed index change in SiC. Additionally, post-radiation relaxation in amorphous SiC does not restore the original pre-irradiated structural state of the material. Our results further point to the potential of realizing radiation-hard photonic device designs taking advantage of the opposite signs of radiation-induced index changes in SiC and ${\mathrm{SiO}}_2$.