Materials enabling impact-energy absorption of high-velocity projectiles are of great interest for applications like aerospace. In such a frame, shear thickening fluids were found very useful. Here, we investigated nanorheological properties of neat and aqueous polyelectrolytes of low molecular weights containing poly([2-(methacryloyloxy) ethyl] trimethyl ammonium) as polycations and poly(acrylamide-co-acrylic acid) as polyanions. Results were compared with pure water. We employed nonequilibrium molecular dynamics with the SLLOD algorithm to compute the viscosity at various shear rates. Systems containing polyelectrolytes exhibit shear thickening. The analysis of molecular configurations revealed a strong disruption of the ionic structure and more clusters with smaller sizes on increasing the shear rate. Potential energies showed that shear thickening originates from an increase in intramolecular and van der Waals interactions resulting from the increasing difficultly of polyelectrolyte-based systems to relax at high shear rates. Our method and findings underscore the importance of accounting for the molecular scale in the design of materials absorbing the impact energy efficiently.