I can definitively state beyon doubt, that shaving absolutely did not cause this. All shaving does is cut the hair at the surface, it does not affect its growth at all.It does notmake the hair courser, that is an old wives tale.
You are right on the money however as to this being related to yu vellus ( downy) hair yes it is related. IT sounds very much like you have experienced paradoxal laser hair stimulation. Sometimes when vellus hair is treated it does not contain any pigment but the dermal papillae is partially damaged. Your body rebuilds it with more blood capillaries and a better blood supply and presto, deeper, darker courser hair.
Solution is 2 fold, first DO NOT do any more laser. The hair can be removed with electrolysis safely with out stimulating the hair further.