I bought a sport harness and a rescue harness. I'm just wondering if i can use them interchangeably.
From a technical standpoint, it depends. For example, for the Petzl Falcon line of rescue harness, only the Mountain is rated fo operations involving technical climbing. The Ascent is not suitable for progression using rock climbing techniques. You will need to carefully read the instructions for your rescue harness to determine its suitability for rock climbing. Sport climbing harnesses lack many of the features (e.g., good padding and compatibility with a chest harness) and durability of rescue harnesses.
From a practical vantage, many SAR teams require dedicated equipment and using your rescue equipment for personal use would be a violation of their policies.