Understanding the mechanical behavior of immune cells as they navigate the complex and confined environment of solid tumors is crucial for improving immunotherapy strategies, such as CAR-T cell treatments. In this work, we introduce a Subcellular Element Model (SEM) that quantitatively links immune cell mechanics, cell deformation under extreme confinement, and migration efficiency, with experimentally validated predictions. We present a particle-based computational framework designed to reproduce the large deformations of single immune cells migrating through narrow microchannels (2, 4, 6, and 8 µm) that mimic tumor micropores, while enabling the evaluation of cell mechanics. The cell is discretized into three main structural components (nucleus, cytoplasm, and membrane) using distinct particle types, whose interactions determine the viscoelastic behavior, accounting for internal resistance and progressive deformation. The model was implemented within the open-source framework PhysiCell, calibrated using Bayesian optimization, and validated by reproducing experimental microfluidic data, achieving prediction errors below 5\% for migration velocity and morphology. Our model also provides a comparative mechanical evaluation between T-cells and CAR-T cells. We found that under conditions of extreme confinement (2 µm microchannels), CAR-T cells exhibit higher stiffness, characterized by larger repulsion constants and internal viscosity, compared to non-engineered T-cells. In contrast, for all other channel sizes, the opposite trend is observed, with T-cells showing greater stiffness. This increased mechanical resistance is associated with lower migration velocities and higher energetic cost. These results suggest that modifications involved in CAR-T production may alter cell mechanics and potentially affect their ability to infiltrate into the tumor core.