How can one find my Instagram if it’s not associated to any of my personal information?

Okay so I sprained my arm and the doctor who did my cast found my Instagram and followed me? But the thing is, my Instagram is private and I don’t have my name on it at all, so I’m really confused. Could he have found it with the phone number on my file or something? I’m trying to keep my social media as private as possible so I'm a little bit disturbed by that.

find my information instagram personal personal information privacy