Morality I think forget the word ‘suing’, it is too value laden and it muddling things up here.
You should complain, via PALS, NHS or private does not matter. That is step one. This is not a judgement. Your case went appallingly wrong and you are entitled to raise this with the hospital authorities and to get answers and appropriate redress including apologies and explanation.
THIS IS NOT A BAD THING THIS IS NORMAL. Never feel guilty about complaining.
Secondly, please see if you can access some advice on seeking damages for the harm you have suffered. There are a lot of ambulance chasing firms so take your time and do a little research before choosing a firm, or talk to a couple. You are so vulnerable so do not be pressured into anything.
It will the the medical lawyers job to look at the case and decide on the notes etc and expert advice on things like negligence but you are certainly someone who I think has been badly damaged and therefore should be entitled to receive a financial payout to reflect the lifelong pain and suffering physical and mental from what has been done to you.
Take the emotion of ‘I shouldn’t sue theNHS out of it’. You are entitled to seek redress for damages.
I am clearly a random on the internet but I do work in a senior position in the NHS so I’m not at all biased against it but this is not acceptable.
I am so so sorry to hear what you have gone through and regardless of what you decide to do, I wish you the best in your ongoing recovery 