I used to work for a lawyer who handled personal-injury suits. See if you can get a lawyer on your side, one who works on a contingency basis.

Sad to say, the doctors and their insurors will probably take no notice of you until you have a lawyer on your side.

Another thing - it wasn't a doctor who put the IV in, was it? It was probably a nurse or nurse's aide. Have the facts clear in your mind before you call the lawyer.