Should I sue? *long post*

I had originally planned on having a vaginal birth. On november 23rd I went into labor... everything was going smoothly and I got the epidural at 6cm. Due to the epidural the contractions slowed down and they started me on pitocin. After a couple of hours they decided to do a csection due to heart rate decreasing during each contraction During the csection I felt every cut and was screaming for them to stop. They completely ignored me and kept cutting. (The baby heart rate was fine at this point) the anesthesiologist came over and told the doctors that they needed to stop so he could give me more medicine or he was going to put me out. They ignored him and continued cutting. At this point the pain from them cutting is so bad I'm screaming i was gonna pass out and puke. I ended up puking several times all over myself. The nurses didnt help and the only thing the anesthesiologist could do was hand my hubby a puke tray. I then feel myself going in and out and finally I was out. I kept coming back to it and going back out again after screaming. The next thing I remember is being in recovery. I spent 2 days in the hospital. I realized my daughter was not moving her left arm. They called in 2 pediatricians to look at her arm. They did an xray (I was not shown it) and they both said they thought it was a muscle strain from delivery. They said it would get better over time. When we were released from the hospital I realized everytime I'd touch her left arm she would cry which told me it was painful. I contacted my chiropractor who is absolutely amazing. He prompted me to request the xrays from the hospital and come in with them. When the chiropractor looked at the xrays and read the xray report he instantly saw they missed her dislocated shoulder. We were confused on how the hell they missed it because it's so clear on the xray. (Xrays of shoulder are down below) The chiropractor had me take pictures of the shoulder and you can see the dislocation in the pictures.

If you were in my situation would you try to sue them or something? I feel I need to do something for my daughter.... I don't really care about me but my daughter could of potentially lost function of her arm forever or been in pain for most of her life because of carelessness of medical professionals.... opinions?