With the persistence of these symptoms, it would indeed be wise to consult with a mental health professional. Your daughter will not be scarred by such an experience. Something is wrong, if you will. It's the behavior, which is injurious to your daughter, that deserves some focus. This will not imply that something is wrong, or inadequate, in her. With such a young child, such behaviors are often meant to reduce tension, though the child may be quite unaware of what is producing the tension. Some children are temperamentally inclined to respond in this manner, even when there are no significant stressors from an objective standpoint.
I would try to get her in therapy. My daughter began tugging on some of her hair when she was 2 1/2, and then did not do it again until she was in the 2nd grade. Then whenever she gets stressed, or anxious, she scratches her head, or tugs on her har.
Some of her hair began falling out. Now she is in third grade, and had begun pulling her eyelashes out. It sounds as if your daughter probably bites her nails and fingertips when she is nervous or anxious, then it became a habit.
The earlier you begin therapy the better, we have been in and out of it with our daughter, and in hindsight, I wish we would have kept it up long term. Now that my daughter is older, she is more aware of going to counseling etc., and I think she is somewhat self consious of it. I wish you the best of luck.