We apply a novel adaptive mesh refinement (AMR) code, AMRVAC (Adaptive Mesh Refinement version of the Versatile Advection Code), to numerically investigate the various evolutionary phases in the interaction of a relativistic shell with its surrounding cold interstellar medium (ISM). We do this for both 1D isotropic and full 2D jet-like fireball models. This is relevant for gamma-ray bursts (GRBs), and we demonstrate that, thanks to the AMR strategy, we resolve the internal structure of the shocked shell-ISM matter, which will leave its imprint on the GRB afterglow. We determine the deceleration from an initial Lorentz factor ? = 100 up to the almost Newtonian phase of the flow. We present axisymmetric 2D shell evolutions, with the 2D extent characterized by their initial opening angle. In such jet-like GRB models, we discuss the differences with the 1D isotropic GRB equivalents. These are mainly due to thermally induced sideways expansions of both the shocked shell and shocked ISM regions. We found that the propagating 2D ultrarelativistic shell does not accrete all the surrounding medium located within its initial opening angle. Part of this ISM matter gets pushed away laterally and forms a wide bow-shock configuration with swirling flow patterns trailing the thin shell. The resulting shell deceleration is quite different from that found in isotropic GRB models. As long as the lateral shell expansion is merely due to ballistic spreading of the shell, isotropic and 2D models agree perfectly. As thermally induced expansions eventually lead to significantly higher lateral speeds, the 2D shell interacts with comparably more ISM matter and decelerates earlier than its isotropic counterpart.