The Non-Orthogonal Multiple Access (NOMA) tech-nique, supported by Intelligent Reflecting Surfaces (IRS), is con-sidered a promising solution to enhance the quality of radio com-munication networks. However, as IRS-NOMA wireless networksare increasingly deployed more densely, inter-cell interferencehas become a significant factor limiting system capacity. Thisissue has not been adequately addressed in most existing IRS-NOMA wireless network research. In this paper, we use a randomgeometry approach to model an uplink DIRS-NOMA densewireless system. Specifically, a group of two users (UE) at the celledge communicates with the base station (BS) through a pair ofIRS, without a direct link to the BS. Based on the proposed model,we develop theoretical frameworks and calculate the BS-IRS-UElink channel statistics using a Rayleigh fading distribution. Wederive the probability density function (PDF) and the cumulativedensity function (CDF). Based on statistical data analysis, wederive closed-form expressions for the outage probability (OP),ergodic rate (ER), and bit error rate (BER) of UEs at the BSas functions of the signal-to-interference-plus-noise ratio (SINR).From the obtained results, we evaluate the overall performanceof the system. We also propose an algorithm that optimizesthe sum rate of all users under individual power constraints.This formulated problem requires simultaneous optimization ofpower at the user and phase shift at the IRS and is non-convex.Finally, we verify the mathematical analysis through comparisonswith Monte Carlo simulations. The presented numerical resultsdemonstrate that the proposed solution achieves near-optimalperformance and outperforms the OMA-based solution in termsof sum rate.