You are quite correct in that there is what is called a statute of limitation of 3 years in which to make a claim, but this statute commences from the date of injury or date of knowledge whichever is the sooner.
So, if your injuries occured for example 5 years ago, but you only found out 1 year ago, then your time would start from the date you became aware of the injury.
Speak to a specialist medical negligence solicitor.
This is a specialist area of law, so don't use any of the claims management firms (for example those who appear on this site telling you to call them, they are a complete waste of space) but go to someone who specialises in medical negligence local to you.
They will give you a free consultation, look at your case and then give you sound and proper advice.
