This work investigates the outage behavior of an uplink non-orthogonal multiple access (NOMA) based mixed underwater optical wireless-RF communication (UOW-RFC) system under dynamic power allocation (DPA) scheme. In particular, we utilize an improved dynamic power allocation (IDPA) scheme over underwater subsystem based on the quality-of-service (QoS) of users and employ partial relaying scheme (PRS) over the RF hop. Moreover, we consider fixed as well as optimum power allocation schemes over the relaying phase. Considering the mixture-Extended Generalized Gamma (mEGG) distribution with pointing error for underwater links and Nakagami-m distribution for RF link, we obtain the expressions for end-to-end outage probability for IDPA scheme in terms of bivariate Fox-H function. It is shown through the numerical results that, in comparison with the conventional DPA (CDPA) and Fixed power allocation (FPA) schemes, IDPA provides significant improvement in the outage performance of both high-QoS and low-QoS users. The numerical results also reveal that employing IDPA enables to overcome the error floor problem of uplink NOMA. The analytical results are corroborated through simulations.