There is no separate bankruptcy called a “medical bankruptcy.” However, I have had many clients forced into bankruptcy solely because of their medical debts. They simply file a normal chapter 7 or chapter 13 bankruptcy.
As for going bankrupt on one kind of debt and excluding the others, no. We are required to list all of your creditors. There are some creditors who receive notice even though the bankruptcy will not affect them (like child support obligations and student loans). There are some creditors who we list and then mark that we intend on reaffirming those debts (signing agreements to maintain liability for those debts). You can even pay back creditors voluntarily after a bankruptcy discharge, but we cannot exclude creditors.
This is not legal advice. If you need help go to www.robertspaynelaw.com.