what is the best way to deal with hospital for negligence?

Recent car accident left me with a 7 day hospital stay. I have three compression fractures in my spine, air bag injury and seatbelt injury to my pelvis with severe abrasions, bruising, internal bleeding/fluid and swelling. the hospital ordered a hard plastic brace to be worn every day, not responding to my complaints of inability to breath and severe rib pain. Three weeks after leaving hospital my orthopedic doctor who is closer to my residence (the hospital was in Tallahassee), re xrayed me as my ribs were still so painful. The hospital report shows no findings of broken ribs, yet my doctor here found seven broken ribs!! An emergency room visit three days after leaving hospital also showed some fractures to my ribs and a partial collapsed lung. I had had a ct scan for intestinal issues at that time and the dr report showed those aswell. I feel that either the hospital was negligent in their treatment and findings or caused the rib fractured from bracing. Do i have a case against them