You’re getting a bit off-track here. The scenario is this: the company that provides the software for your care collects data. This part is unconcerned with Amendment 4. Amendment 4 prohibits the State from collecting information and searching unreasonably. It does not prohibit the private company that provides the software from doing so. That is what privacy laws are intended to protect against, not Amendment 4.
Amendment 4 also does not prevent the company that collected that data from providing it to the police upon request. Amendment 4 (and the rest of the US Constitution) applies only to the State. Private companies and private individuals are not bound by it.