Nowadays all medical records are electronic and housed on a network for that practice's office. Most doctors have affiliation with a local hospital and they typically share a network of medical records so that, for example, if you go get an MRI or blood work at the hospital, your doctor will be able to see the results at their office.
All that being said, there is not one central dumping ground for everyone's medical records. Such a thing does not exist. So if this woman is not affiliated with your doctor's office nor the hospital that your doctor is affiliated with, then there is no way for her to get a hold of your records.
Furthermore, HIPAA laws are actually very strict and violation of these privacy laws related to medical records is punishable by extremely high fines and jail time. Only a complete idiot would break those rules.
One in Four Americans have been on an antidepressant. No shame in it. Really. I wish the stigma would disappear as people try to help themselves feel better. We treat all other illnesses but somehow someone feels embarrassed that they were diagnosed with and got treatment for depression.
As stated, just because someone is a doctor, they don't have access to all the medical records of another person unless they are in direct relationship with their care.
However, you re starting a relationship with secrets. That is never good. You don't have to divulge it outright but you should not be afraid to let a partner that has future long term potential finding out who you are and what you've been through in life. And once married, I signed a paper that my husband does have access to my medical records/information. This is pretty common when you sign the HIPPA agreement every year to designate a loved one which is usually your significant other to be someone that can have knowledge of any health related thing going on with you. My husband has never looked, called the office to know, etc. But he could if he wanted or needed to in the case of some catastrophe with my health and I was unable to care for myself.
Just food for thought. good luck