There are a few things that have a large effect on this question. First is the toxicity of the hair. In your question, it seemed to be pretty severe, starting with paralysis and ending with death. Second is our ability to diagnose and treat this toxin. Is it something we know about? Is it something we can treat easily and successfully? If this is not the case, then I will need to change my answer.
Her mother will either die before she could be born, or she will become very sick, have an abortion, and possibly survive. Babies have hair at least as early as the 16th week of gestation, and many of the body's defenses would already have been bypassed. Her mother would become sick a few months after becoming pregnant, and would likely die before the doctors could identify the problem, identify the toxin, acquire the antidote/treat it, and induce an abortion.
Perhaps you can find a way to set it so that she does not exhibit this phenomena until she is born. Then, it is likely that she will survive. Again, depending on how discoverable, dangerous, and treatable this toxin is, she may kill her mother, father, nursemaid, and any other number of people.
However, it would be relatively easy to avoid that, as a storyteller. Her mother takes sick while still in the hospital, after holding her newborn child. When the hospital notices that everyone who has come into extended contact with the baby is falling ill, they may isolate the child, much in the way that preemies are isolated, but for the opposite reason. It would be difficult to raise a child in this manner, and would necessitate certain unfortunate precautions such as limited physical contact or the removal of most hair.
Your character would likely never be able to grow her hair out. Hair is shed naturally by humans, and hair particulate can still escape from hair that "up", in a hair net, etc. This loose hair could bother someone, cause substantial harm when inhaled, or kill an asthmatic child or elderly person.
However, she could and should live a normal life by shaving her head and managing the rest of her hair, either through covering it with clothing or removing it through normal techniques. She should shave her hair regularly (daily? maybe, maybe not), using a shaving tool and a vacuum attachment and then safely disposing of her hair.
Given that she does not exhibit hair toxicity in utero, then it is certainly possible that she lives a life that is long and rewarding for her. She will grow up with this limitation, which may cause the parents stress and make for a difficult childhood depending on her temperment (up to you) and living situation, but she can live a long and rewarding life, competing in sports and the arts, going to high school and college, finding a normal job and working, dating and getting married, the whole nine yards.
Or she could run away from her parents at age 16 and slip between the cracks, living as a runaway in a major city, growing her hair out in rebellion from a life she didn't choose, leaving in her wake a trail of quiet death from respiratory failure. The choice is up to you, but I hope for her sake she is happy.