Fused Filament Fabrication is an additive manufacturing technique in which molten thermoplastic polymers are extruded through a nozzle. Therefore, the interplay between the viscoelastic nature of the polymer melt, temperature, printing conditions and nozzle shape may lead to inconsistent extrusion. To improve the extrusion control and optimize the print-head performance, a better understanding of the flow process of the polymer melt both in the nozzle and the liquefier is needed. However, several challenges need to be overcome due to the complexity of gathering experimental data on the melt pressure in the nozzle and the lack of numerical models able to capture the full rheology of the molten polymer. This research introduces an innovative approach for monitoring the pressure within a material extrusion 3D printer's nozzle. This method involves utilizing a pin in direct contact with the molten material, which then transmits the applied force from the material to an externally mounted load cell. The setup provides reliable, repeatable pressure data in steady-state conditions for two nozzle geometries and at different extrusion flows and temperatures. Moreover, the Giesekus model enabled capturing the viscoelastic rheometric features of the melt, and the numerical predictions have been compared with the experimental data. Results show that the numerical model accurately describes the flow conditions in the nozzle and allows the estimation of the behavior of the melt in the liquefier zone, the area of the print-head where the filament is molten. It could be concluded that the backflow, which is the backward flow of the molten polymer in the gap between the filament and the liquefier towards the cold end, caused significant non-linearities in the total pressure drop measured in the feeders, which were related to normal forces induced by shear in that region.