If your goal is that ever person is unique accross your application, email is not a suitable constraint of uniqueness. Some people do not have an email address, some people share an email address (e.g. couples), and some people have multiple email addresses.
In the USA, the best unique constraint, and the one I most often see with banks, insurance, background checks, etc. is social security number (SSN) + birthdate. Social security numbers are assigned to US citizens, residents and temporary workers. They're recycled after a person dies, so it's not good enough on its own. You should be careful about how you store SSNs. You should treat them as protected information because they can be used to steal a person's identity. They should not be stored in plaintext in a database. Further, patients and health providers may be reluctant to share this information with your system.
It's possible, however, in the health system for patients to be undocumented or otherwise not have a social security number. You may want to support this case in your system.