I agree with Lemon Pie that this is most likely an immune response. I have autoimmune disease with sky high antinuclear antibodies. Specifically my anticentromere B antibodies are literally off-the-chart high. These are noted for causing inflammation of small blood vessels.
Just as you describe, I have developed these white spots all over my forearms, and many of them have a tiny red dot in the center, which blanches under pressure. I believe that a vasculitis in these small blood vessels causes a surrounding loss of pigment in the skin.
Perhaps related to this, I have also developed a burning neuropathy in my hands and feet, and have discovered that heat triggers the soles of my feet and palmar surfaces of my hands to become flaming red, with intensification of the burning. It is especially bad under covers during the night (it wakes me with pain), and when standing in one place, and when I get too warm. One of my doctors says that's called erythromelalgia. I am also being checked for Fabry Disease.
Please get to a rheumatologist and ask to be checked for antinuclear antibodies, particularly the separate test for anticentromere antibodies.