One effective method for reducing pressure drop in turbulent pipe flows is the injection of Drag Reducing Agents (DRA), a technique that has been used for over 70 years. This study investigated the modeling and simulation of turbulent pipe flow behavior by developing a novel k-ω turbulence model and utilizing the modified Generalized Newtonian Fluid (GNF) model to integrate the fluid's rheological properties. The focus was on turbulent pipe flows involving DRA, which exhibit viscoelastic non-Newtonian fluid properties. This new k-ω model was derived from mathematical modeling by using the non-Newtonian k-ε model. Computational Fluid Dynamics (CFD) software was used to simulate the derived equations, incorporating non-Newtonian terms that encompass the rheological properties of drag-reducing fluids. These terms were implemented into the software using User-Defined Functions (UDFs). To assess the accuracy of our results, we compared them with data from the open literature, demonstrating a significant improvement in the precision of our results. Our model exhibited good agreement with experimental data, with an average deviation of 10.53% in the friction factor predicted for the studied fluids. Furthermore, the model showed high accuracy in near-wall regions, particularly the viscous and buffer sublayers.