My Doberman is licking it's - tail area, best answer to the best post,?

We rescued this Doberman at 3 months and her previous owners already had her tail docked, A procedure I do not agree with. She is now one year and a half old. For 3 days now she has being licking this area more frequently in an 'outburst' manor, I have read about worms and swelling of glands, it is not swolling and she is not dragging on the floor, i examined what used to be her tail and noticed a black discoloration at the stump. She slightly reacted when i touched the skin. I'm not sure if this black patch usually appears on the end of an amputation on a Doberman so I don't know if I should be alarmed and take her to the vet. Shes not in a lot of pain but as I say this only started 3 days ago. I'm also wondering if improper docking can cause long term damage to the inner tissue of the tail, and therefor cause the dog to feel at discomfort. just to add, she has all her tablets and jags to date. Thanks and hope some of you can answer,