Rapid evolution of wireless medical devices and network technologies has fostered the growth of remote monitoring systems. Such new technologies enable monitoring patients' medical records anytime and anywhere without limiting patients' activities. However, critical challenges have emerged with remote monitoring systems due to the enormous amount of generated data that need to be efficiently processed and wirelessly transmitted to the service providers in time. Thus, in this paper, we leverage full-duplex capabilities for fast transmission, while tackling the trade-off between Quality of Service (QoS) requirements and consequent self-interference (SI) for efficient remote monitoring healthcare systems. The proposed framework jointly considers the residual SI resulting from simultaneous transmission and reception along with the compressibility feature of medical data in order to optimize the data transmission over wireless channels, while maintaining the application's QoS constraint. Our simulation results demonstrate the efficiency of the proposed solution in terms of minimizing the transmission power, residual self-interference, and encoding distortion.