Non-orthogonal multiple access (NOMA) and spectrum sharing (SS) are two emerging multiple access technologies for efficient spectrum utilization in future wireless communications standards. In this paper, we present the performance analysis of a NOMA-based cooperative relaying system (CRS) in an underlay spectrum sharing scenario, considering a peak interference constraint (PIC), where the peak interference inflicted by the secondary (unlicensed) network on the primary-user (licensed) receiver (PU-Rx) should be less than a predetermined threshold. In the proposed system the relay and the secondary-user receiver (SU-Rx) are equipped with multiple receive antennas and apply selection combining (SC), where the antenna with highest instantaneous signal-to-noise ratio (SNR) is selected, and maximal-ratio combining (MRC), for signal reception. Closed-form expressions are derived for the average achievable rate and outage probabilities for SS-based CRS-NOMA. These results show that for large values of peak interference power, the SS-based CRS-NOMA outperforms the CRS with conventional orthogonal multiple access (OMA) in terms of spectral efficiency. The effect of the interference channel on the system performance is also discussed, and in particular, it is shown that the interference channel between the secondary-user transmitter (SU-Tx) and the PU-Rx has a more severe effect on the average achievable rate as compared to that between the relay and the PU-Rx. A close agreement between the analytical and numerical results confirm the correctness of our rate and outage analysis.