Space confinement greatly influences the properties of liquids, such as their viscosity and capillary critical point. For aqueous solutions of amphiphiles, this effect is extended to the mobility and micellization properties of these molecules, changing important characteristics of micellar solutions such as the critical micelle concentration (CMC). In the present work, we use a lattice Monte Carlo model, which allows for orientational freedom and hydrogen-bond formation for the water molecules, to investigate confinement effects on a solution of surfactants limited by two parallel walls perpendicular to one of the Cartesian axes. This configuration aims to reproduce a small pore, and walls with a hydrophilic or hydrophobic character are studied. We find that, for hydrophilic walls, there is an increase in the value of the CMC for small pores, caused by space confinement effects and also by the interactions of the amphiphile polar heads with the walls. Micelles are able to adhere to the walls as a whole, and their shape shows little change compared to micelles in the bulk solution. Hydrophobic walls show a more dramatic effect on the properties of the solution, arising mainly from the strong adsorption of the amphiphile tails on the walls, driven by the hydrophobic effect. The process of adsorption of amphiphiles with increasing concentration shows a behavior very similar to the one observed in experiments and simulations of such systems. Micelles adsorbed to the hydrophobic walls also show significant changes in their moments of inertia compared to the bulk ones, which is attributed to the formation of half-micelles that have their tails attached to the walls and the polar heads facing the solution. We extend our analysis to the change in the hydrogen-bonding properties of the solvent caused by the confinement, and how that is directly related to the number of free amphiphiles in our system for different pore sizes. Finally, we test different surfactant sizes and how they affect the micellar shape for different concentrations.