Can I file a case against my doctor for missing a fracture in an X-ray?

I was in a motorcycle crash and was admitted to the hospital. X-rays were taken the same day and I was treated for a broken left tibia plateau, broken right distal radius, and a partially amputated left index finger. I noticed several weeks later that the knuckles on my left hand looked strange and had pain in my left hand that seemed abnormal I saw my orthopedic surgeon for a follow up and asked about my left hand. He did X-rays and found that my hand had also been broken on and was now improperly healed. He admitted to missing the fracture the first time X-rays were taken. Now I have to wait for my other injuries to fully heal before the doctor can go in and re-break the bones and set them with pins. I currently have pain and very little strength in my left hand and can't bend my fingers back very far.