Any government agent intruding on your privacy is a violation of the 3RD amendment. The purpose for not quartering soldiers in your home is so that a government employee or agent cannot gather information about you and your family.
If the government mandates a doctor to conduct this intelligence gathering then that is a 3rd amendment violation against your right to privacy.
"The whole of the Bill (of Rights) is a declaration of the right of the people at large or considered as individuals .... It establishes some rights of the individual as unalienable and which consequently, no majority has a right to deprive them of."-- Albert Gallatin, New York Historical Society, October 7, 1789