I am sorry to hear about your daughter's arm. There is a legal principle applicable to your daughter's case - "The Defendant takes the Plaintiff as he finds him". This means that it does not matter that the plaintiff had a problem to begin with; if the plaintiff did something to worsen the condition, the Defendant is still liable to the Plaintiff.
For example, let us assume that a paraplegic was in an automobile accident and the other driver was at fault. The injuries sustained by the paraplegic resulted in his becoming a quadriplegic. The Defendant cannot say, "Well, you can't hold me liable because he couldn't walk even before the accident, so what's the difference now?" The fact that the other driver's negligence caused the Plainiff's condition to worsen, makes the Defendant liable to the Plaintiff for making his condition worse.
Therefore, if these Attorneys you have spoken to have the idea that your daughter's case is not worth much because she only had little function before the malpractice, they are totally out in left field.
In Answer to your question, "Yes" you can pay an Attorney to represent your daughter in the malpractice case. Just because a majority of personal injury cases are taken on contingent fee, does not mean that you cannot hire an Attorney and pay him to take the case. You should call your State and County Bar Association Lawyer Referral Services, tell them what your situation is, and ask for the names of several Attorneys who have experience in malpractice litigation cases.
I wish you and your daughter, the very best of luck,
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