We obtained 420 high-resolution spectra of Proxima, over 159 nights, using the Near Infra Red Planet Searcher (NIRPS). We derived 149 nightly binned radial velocity measurements with a standard deviation of 1.69m/s and a median uncertainty of 55cm/s, and performed a joint analysis combining radial velocities, spectroscopic activity indicators, and ground-based photometry, to model the planetary and stellar signals present in the data, applying multi-dimensional Gaussian process regression to model the activity signals. We detect the radial velocity signal of Proxima b in the NIRPS data. All planetary characteristics are consistent with those previously derived using visible light spectrographs. In addition, we find evidence of the presence of the sub-Earth Proxima d in the NIRPS data. When combining the data with the HARPS observations taken simultaneous to NIRPS, we obtain a tentative detection of Proxima d and parameters consistent with those measured with ESPRESSO. By combining the NIRPS data with simultaneously obtained HARPS observations and archival data, we confirm the existence of Proxima d, and demonstrate that its parameters are stable over time and against change of instrument. We refine the planetary parameters of Proxima b and d, and find inconclusive evidence of the signal attributed to Proxima c (P=1900d) being present in the data. We measure Proxima b and d to have minimum masses of 1.055+/-0.055M_{Earth}, and 0.260+/-0.038M{Earth}_, respectively. Our results show that, in the case of Proxima, NIRPS provides more precise radial velocity data than HARPS, and a more significant detection of the planetary signals. The standard deviation of the residuals of NIRPS after the fit is ~80cm/s, showcasing the potential of NIRPS to measure precise radial velocities in the near-infrared.