I told my ob that I had an induced abortion. Are doctors allowed to tell it to my healthcare insurance? She did. And I felt humiliated.

Unfortunately yes. Doctors are obliged to document all pertinent medical history in your chart, because it's relevant. Unfortunately Insurance companies have the right to have access to your chart whenever they want. So Doctors do not have choice, unless you sign a letter with your Doctors office telling not to give any information to your Insurance and you are legally responsible for the consequences .