The effect of quantum electrodynamic effects like radiation reaction and pair production on shock formation and subsequent ion acceleration from laser-plasma interaction are explored by means of particle-in-cell simulations. In this setup, the incident laser pushes the laser-plasma interface inside the plasma target through the hole-boring effect and generates hot electrons. The propagation of these hot electrons inside the target excites a return plasma current, leading to filamentary structures caused by the Weibel/filamentation instability which eventually leads to the formation of shock. In the ultra-relativistic regime, both radiation reaction and pair plasma formation tend to slow down the shock velocity which makes the quasi-monoenergetic ion acceleration lasting on longer timescales.