In this paper, we consider a novel underlay relayed non-orthogonal multiple access (NOMA) network with cooperative relaying by an energy harvesting (EH) near-user ( NU) so to improve the performance of a far-user ( FU) without requiring the NU to expend its own battery energy. The NU is assumed to harvest energy from the relay using the power-splitting protocol. Expressions are derived for end-to-end outage probability and throughput of both NU and FU. Although the source, relay and NU limit their transmit powers to ensure that the peak interference caused to the primary is below the interference temperature limit (ITL), the network still performs better than orthogonal multiple access (OMA) based network. We show that combining of signals from relay and NU ensures good FU performance in this power constrained scenario. We demonstrate that both NOMA power allocation parameter as well as the energy harvesting parameter need to be chosen carefully to maximize the sum throughput. Simulation results corroborate the derived analytical expressions.