In this work, we investigate reconfigurable intelligent surface (RIS)-assisted Cooperative non-Orthogonal Multiple Access (C-NOMA) consisting of two paired devices. The device with better channel conditions (D1) is designated to act as a full-duplex (FD) relay to assist the device with poor channel conditions (D2). D1 does not use its battery energy to cooperate but harvests energy using Simultaneous Wireless Information Power Transfer (SWIPT). A practical non-linear Energy Harvesting (EH) model is consid- ered. We assume that all devices’ links undergo Nakagami-m channel fading. We first approximate the harvested power as Gamma random variables via the Moment Matching (MM) technique. This allows us to derive analytical expressions for Outage Probability (OP) and ergodic rate (ER) that are simple to compute yet accurate for a wide range of RIS passive elements configurations, EH coefficients, and residual Self Interference (SI) levels, being extensively validated by numerical simulations. The OP expressions reveal how important it is to mitigate the SI in the FD relay mode since, for reasonable values of residual SI coefficient, it is notable its detrimental effect on the system performance. Also, numerical results reveal that increasing the number of RIS elements can benefit the cooperative system much more than the non-cooperative one.