Nonreciprocal transmission is the fundamental process behind unidirectional wave propagation phenomena. In our work, a compact and practical parity-time (PT) symmetric metamaterial is designed based on two Silicon Carbide (SiC) media separated by an air gap and photonically doped with gain and loss defects. We demonstrate that an exceptional point (EP) is formed in this PT-symmetric system when SiC operates as a practical epsilon-near-zero (ENZ) material and by taking into account its moderate optical loss. Furthermore and even more importantly, strong self-induced nonreciprocal transmission is excited due to the nonlinear Kerr effect at a frequency slightly shifted off the EP but without breaking the PT-symmetric phase. The transmittance from one direction is exactly unity while the transmittance from the other direction is decreased to very low values, achieving very high optical isolation. The proposed active nonlinear metamaterial overcomes the fundamental physical bounds on nonreciprocity compared with a passive nonlinear nonreciprocal resonator. The strong self-induced nonreciprocal transmission arises from the extreme asymmetric field distribution achieved upon excitation from opposite incident directions. The significant enhancement of the electric field in the defects effectively decreases the required optical power to trigger the presented nonlinear response. This work can have a plethora of applications, such as nonreciprocal ultrathin coatings for the protection of sources or other sensitive equipment from external pulsed signals, circulators, and isolators.