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This paper investigates short-packet communications (SPCs) of a cooperative non-orthogonal multiple access (NOMA) Internet-of-Things (IoT)-based cellular network where an IoT master node acts as: (1) a relay for the cellular system and (2) a source for the IoT system. Accurate and asymptotic closed-form expressions for the average block error rates (BLERs) of cellular user (CU) and IoT user (IU) are derived in the presence of imperfect successive interference cancellation (SIC) and channel state information (CSI). Notably, numerical results show that: (i) IUs' performance is significantly improved by exploitation of NOMA technique and is not dominated by decode-and-forward (DF) or amplify-and-forward (AF) relaying protocol; (ii) CUs' performance may not perform well compared with orthogonal multiple access (OMA)-based systems for both AF and DF protocols; (iii) higher antenna configuration at the cellular …