Leaving people off the list is lying to the court. You do NOT want to lie to the court.
Your hospital is an enormous operation who will neither know nor case that you filed bankruptcy.
Your personal doctor is another issue. If you have some time to work with, see if you can pay him off before you finish paying your lawyer. Or go talk to his office manager, and work out a plan to keep paying after you file the bankruptcy. You are allowed to pay anyone you want to pay; you are not allowed to leave people off the list.
Yes you have to add it, also if you delay your filing until after you incur the additional medical debt, you can include that debt in your bankruptcy.