I paid my last attorney around $250 per hour and was very satisfied. Something like this might only be a couple of hours. Have an initial meeting with the attorney (usually free). They'll develop a strategy with you, in this case it would probably be to document the situation and send a letter explaining that a lawyer is engaged. Then the whole thing might stop there.

Some attorneys will actually answer the phone and have a small conversation. Maybe it's rare or different for healthcare issues, but I've made that phone call before. I politely asked a few questions and that was it.