Accelerometers based on triboelectric nanogenerators (TENGs) have been widely reported in recent years. However, most of them lack a self-sustained power supply used for autonomous wireless operation, as well as a mechanism for over-range detection. Additionally, there is a scarcity of theoretical studies of sensitivity of TENG-based accelerometers. In this work, a novel self-sustainable accelerometer for vibration and shock integrating a freestanding triboelectric-layer-based TENG (FT-TENG), two contact-separation TENGs (CS-TENGs) and an electromagnetic generator (EMG) is proposed and then explored through both mathematic simulations and experimental demonstrations. The EMG serves as a power supply for the whole sensor system, which can achieve a power of 4.11 mW under a vibration acceleration of 12 m/s2. The FT-TENG and the two CS-TENGs work for acceleration sensing and over-range detection respectively. Under vibration, the sensitivity and measurement range are found to be correlated with the vibration frequency, and the proposed accelerometer has the maximum sensitivity (0.75 V·s2/m) at its natural frequency. For shock events, the sensitivity of the accelerometer is dominated by the shock duration in a short-duration range, which is estimated to be 0.12 V·s2/m under a shock duration of 0.03 s during shock testing. This work opens up new avenues for potential applications of triboelectric and electromagnetic energy harvesting and provides a feasible design for autonomous wireless sensor nodes.