Should I write a letter of complaint to the hospital before making a claim for clinical negligence?

At the beginner of last year I fractured my wrist and needed pins to stabilise the wrist. I went back to the hospital 5 weeks later in a lot of pain. They examined me and sent me away. Over the next few weeks I went back to the hospital several times as my finger was extremely swollen, I was in a lot of pain and felt ill. They finally took the pin out and sent me away. The following day I ended up back in the hospital and put on a drip after they realised it was sepsis.

Over the past year I have had multiple operations and have lost the use of my little finger, which has been left in a permanent hook position. I have now been told that there is nothing more that they can do, and I will have to have the finger and part of my hand amputated.

I have seen 2 specialists who have both said that several mistakes had been made with both the aftercare after my original operation, and the subsequent operations I went through.

My question is, should I first write a letter of complaint to the hospital or request answers as to why certain things weren't done before I start a clinical negligence claim? Or is this something that I should leave in the hands of a solicitor?