Solidworks and fusion 360 are a bit of a different beast in terms of modelling. They are nurbs based, where game modeling is based on polygons.
You can slightly get around this with using zbrush where you can sculpt without worry of polygons, but in the end you will have to do a retopoly pass where the final polygon mesh will have to be made.
Blender also has a sculpt mode though it’s not as optimized as zbrush (but it’s getting closer with each update).
But at least you probably have had experience with some of the ui concepts that will carry over to other software.
Blender and zbrush are a bit out an outsider in this regard as they have their own shortcuts.
Drawing will defiantly help with sculpting if you have a graphics tablet.