Legal help - writing a demand letter for medical malpractice

My son suffered disfiguring injury which could have been prevented if it was properly diagnosed.  I spoke with a lawyer (this was 2 years ago) and they agreed at first to take the case, told me about how much we could possibly be awarded, then later when I hesitated to hire him, he changed his mind.  A few other lawyers have since said that the amount that they'd get would not be worth it for us to get anything out of it.  My son is now 18 and he wants to seek restitution.  I'm looking for help to do this on my own - to write a letter to the insurance company to demand compensation. I have all the medical records.  I mostly need to know where to send the letter - I've started to write it based on examples I've seen online.  I'm also open if I can afford to, to paying for a lawyer to draft the letter for me, by the hour.  So please if you can't help but can recommend a lawyer with a reasonably per-hour rate for letter writing, I'd appreciate the recommendations.