Are Brown Spots and Freckling Permanent After Laser Hair Removal?

The brown spots on your photo look like freckles that darkened after laser hair removal.  The brown spots/freckles also contain melanin, like hair does.  When a light source like IPL for example hits a brown spot, the pigment in the brown spot darkens initially, then breaks down into coffee grounds, then disappears.

I would wait probably two weeks or so before deciding whether anything needs to be done about the brown spots.  They may disappear on their own.

These don't look like laser burns because they don't correspond to the geometric shape of a laser piece that comes in contact with the skin.  If this would be post-inflammatory hyperpigmentation, then a fading cream might help.

The spots appearing so early may mean that this represents bruising so it may go away in about a week. You should use sunscreen every day and wash your face gently with mild soap and cool water. Don't use skin lightening products on this. Your skin is more susceptible to  additional injury immediately after the LHR.

Hope you are better by now!