I dont think that it is caused from colouring your hair.skin problems like acne,whiteheads arises when your blood is impure.liver is directly concerned for skin problems.cure your liver and your skin will be cured by itself.drink a lot and lot of water everyday,esp when u wake up in the morning
If you are old enough to color grey hair you may actually have dry skin. Have you tried using an exfoliating skin cleanser for older skin a few times a week? You may have dry skin blocking your pores. You should be moisturizing every day too. Seeing a doctor or dermatologist would be the best bet.
This is not really an answer, but has to do with hair color: Once my wife found some blond hair on my shirt and she suspected that I was having an affair with a blonde. When she found red hair, she was furious. Weeks passed and she did not find any hair. She became even madder. She said I was dating a bald lady.