Vehicular communications, with their promise to provide drivers and passengers with a wide range of applications, are attracting significant attention from both research and industry. In this paper, we study the performance of full duplex amplify and forward (AF) relaying-based vehicle-to-vehicle (V2V) cooperative wireless communications over Nakagami- $m$ fading channels. In such systems, in practical scenarios, the communication link inevitably suffers from co-channel interference, residual self-interference, and blockage from other vehicles on the road. In this context, we consider independent and not necessarily identically distributed (i.n.i.d) Nakagami- $m$ fading channels and derive novel exact and asymptotic outage probabilities of the exact equivalent and approximated signal-to-interference-plus-noise ratio (SINR), respectively. Building on this, the end-to-end exact and asymptotic outage probabilities are expressed in terms of the blockage probability and then used to evaluate the throughput of the proposed system. In addition, a lower bound to the symbol error rate of the considered system is also derived. Monte-Carlo simulation results are provided to demonstrate the accuracy of the proposed analytical expressions. The results demonstrate the significant impact of the considered interference and blockage on the system performance. Precisely, it is shown that the system performance is degraded when the average height of the obstacles is increased. This highlights the importance of taking into account these phenomena in the performance evaluation in order to assess the practical limit of V2V cooperative wireless communications.