Endoscopy, in medical sciences, is a modern mechanism for the examination of internal remote organs by the direct insertion of the illuminated tube inside the body. It also transports the fluid with the movement of contraction and relaxation. The current study aims to explore the peristaltic propulsion of ethylene glycol-based graphene oxide nanofluid through an endoscope. The considered nanofluid depicts shear-thinning aspects, which are described by the Carreau–Yasuda fluid model. The modified Darcy's law is employed to describe the porosity of the medium. For a precise calculation, the modified Buongiorno model is adopted with the incorporated Maxwell's model, Brownian motion parameter, and variable for the thermophoresis effect. The mathematical problem linearized under the lubrication approach is solved numerically through Mathematica. After using the experimentally found values of Carreau–Yasuda fluid parameters for different levels of nanoparticle proportion, It is concluded that there is a slight decline in the velocity and the temperature of the nanofluid. Furthermore, a larger Biot number contributes significantly to the heat transfer coefficient. Fluid flow is assisted by a rise in the Darcy porosity parameter. For an increment in the strength of the buoyancy forces, there is a significant uplift in the fluid's temperature and the velocity.