Medical data sensors on patients in hospitals produce an increasingly large volume of increasingly diverse real-time data. Because scheduling the transmission of this data through wireless hospital networks becomes a crucial problem, we propose a Reinforcement Learning-based queue management and scheduling scheme. In this scheme, we use a game-theoretical approach where patients compete for transmission resources by assigning different utility values to data packets. These utility functions are largely based on data criticality and deadline, which together determine the data's scheduling priority. Simulation results demonstrate the high performance of this scheme in comparison to a datatype-based scheme, with the drop rate of critical data as a performance measure. We also show how patients can optimize their policies based on the utility functions of competing patients.