In this paper, we investigate the non-linear energy harvesting (EH)-based unmanned aerial vehicle (UAV)-assisted full-duplex (FD) Internet-of-Things (IoT) network with infinite and finite blocklength (FBL) codes. The reliability performance of the considered network, having two half-duplex UAVs and an FD IoT device, is analyzed in terms of block error rate (BLER) with given ultra-reliable and low-latency communication constraints. With the assumption of the combined effect of fading and shadowing, the closed-form expressions for BLER and network goodput are obtained over Rician shadowed fading channels considering various shadowing scenarios, EH receiver architecture, IoT device mobility, inter-UAV interference, and self-interference (SI) cancellation capabilities at FD IoT device. The obtained results over Rician shadowed fading for non-linear EH receiver architecture are also compared with the linear EH and over Rician fading channels. The numerical results reveal important observations related to the impact of time-selective fading channels with imperfect channel state information, shadowing severity in the suburban areas, SI cancellation capabilities, blocklength and number of channel uses on the reliability performance of the UAV-assisted FD IoT network. Furthermore, the tightness of the approximation presented is verified through Monte-Carlo simulations.