This paper examines the effect of the Intelligent Reflecting Surface (IRS) inclusion on the performance of uplink non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) schemes in wireless systems. NOMA is seen as an important technology for next-generation wireless networks, especially since demand for spectral efficiency will be increasing. However, several challenges exist with regard to the uplink scenario such as inter-user interference and power allocation. Utilizing IRS technology gives this system an edge where the phase of arriving electromagnetic waves can be altered which improves signal reception while minimizing interference. Despite this, analysis through simulation shows that in the uplink case, OMA can be said to provide greater data rates and outperforms NOMA in terms of system efficiency overall, especially in scenarios where IRS is present. It is observed also that as the number of IRS reflecting elements increases, the gap on system performance increases as well. These results enable important considerations for the improvement of next-generation wireless networks including scenarios for 5G, 6G and other successive generations of networks where NOMA is considered a superior technology to the advanced OMA.