Because you live in Alabama, I am assuming the case also involves treatment of your child in Alabama. Since I am not an Alabama lawyer, I cannot specifically advise you on Alabama law but can tell you a bit about principles generally applicable to malpractice cases. If you have specific questions about your rights, you should talk with an attorney licensed in Alabama.
In general terms, a malpractice case can be brought when a doctor is negligent and that negligence results in damages. You must generally show that a doctor was negligent by having another medical doctor review the case and provide testimony (or sometimes an affidavit) indicating that the treating doctor was negligent and that this negligence caused the child's injury. This can be costly because few medical experts work for free. As a general rule, unless there is significant permanent injury, I generally counsel people to be very cautious about bringing a medical malpractice claim. The costs of the suit (including medical experts) together with attorney's fees can sometimes far outweigh the potential damages you could hope to recover. You may also want to give some thought to filing a written complaint with the licensing board in your state which licenses medical doctors. Once again, however, if you are serious about having this claim evaluated under Alabama law, you should seek specific guidance from an Alabama lawyer.
A roundup of the best tips and legal advice.