does hospital need to let you know that the doctor practicing on you has no malpractice insurance incase something goes wrong

Hello . I have question because i find my self sometimes unable to sleep at night . Its been five years now and i know to bring a malpractice casein Florida regarding a minor you have until the child eight birthday. I tried this before when he was about a year but the organization NICA who would be representing me told me they couldnt because the doctor had no malpractice insurance so i left it at that but until this day it still bothers me because my son has chronic asthma althogh he beats all odd against all neurological issues with the help of thearpy i still wonder about him. I still wonder if his respirstory distress at birth is link to his asthma. Also i wonder if the hospital should be responsible for letting me the patient know