In this paper, we analyze the performance of a full-duplex (FD) cooperative non-orthogonal multiple access (C-NOMA) relaying system with an amplify-and-forward (AF) protocol in the presence of loopback interference in FD transceivers. Particularly, by considering channel estimation errors and quantization noise in low-resolution analog-to-digital converters (ADCs), the accurate approximation expression for the ergodic rate and closed-form solution for the outage probability are derived, respectively. The validity of the theoretical results is verified by Monte Carlo simulations, which show that both channel estimation errors and quantization noise have deleterious effects on ergodic rate and outage performance for moderate and high signal-to-noise ratios (SNR). In the second phase of the C-NOMA system, both the outage performance and ergodic sum rate decrease at high SNRs due to the effects of loop interference. When the ADC dynamic range reaches a certain level, the system performance is more affected by loopback interference and channel estimation errors compared to the quantization noise of the ADCs.