No projection is natively going to give you the correct distances unless you are measuring very particular lines, like from the center of a azimuthal equidistant projection.
If the area of interest is relatively small, a projected coordinate reference system (CRS) that's conformal (maintains local angles/shapes) or equal area may give 'good enough' results.
Some software tools or workflows may have the capability to return geodesic-based distances instead. Geodesic distances are based on the surface of the ellipsoid so still not 100% correct relative to the topography, but often good enough versus 2D Cartesian distances based on a projected CRS.
For half of South America, you could make a custom equidistant cylindrical projection. That would have accurate north-south distances and the distances along the standard parallels would be accurate. Use SIRGAS for the geographic CRS.