I made a map of a tidally-locked world under the premise that I was drawing it as an Azimuthal Projection, or a Planar Projection or something like that (I'm afraid I don't know the difference). This map is centered on the substellar point, where the star shines directly. I've been experimenting for some time on how to redraw this map as an equirectangular projection so that I can wrap it around a sphere in a program such as Google Earth, so that I can more easily visualize things like climates and winds. I have tried redrawing it by eye on a square half of a 1:2 rectangle, but I have not been able to master the way in which the circular gradations of distance from the substellar point (imagine them as circles of latitude, but originating from a point on the equator instead of the pole) slowly warp into a square as they approach the edges.
I've been using GIMP for this, and although I have searched the program for a tool to morph a circular image into a square one, I have not found one. Even if I had, this wouldn't be enough, since things get weird at the poles of equirectangular projections.
I have next to no experience in coding, and I don't know anything about how map projections work mathematically, and so any tips about programs I can use, methods I can employ, or resources I can consult are greatly appreciated.