I burned 3 of my fingers by accidentally putting my hand on a coil stovetop burner. this was about 4-5 hours ago. the burned skin is white, not blistering. im also still experiencing quite painful burning sensation in my fingers. what should i do?

Place the area that is burned under cold running water immediately. This will help take the heat out of the tissue slowing the destruction of soft tissue by the heat. If blisters form use antibiotic Ointment

If the burns are not blistered and the they did not wrap around your entire finger(s), then the typical treatment would be antibiotics ointment and a soft bandage for the first week or so and then just moisturizer. Do not shy away from using your hand or fingers to make a fist though so that the joints do not get stiff during the healing process. I hope this helps!