Tricia, first it is so very good that you are completely open to your feelings when alone.
Yes, doctors are people. They are also professionals. They are bound to the oaths of the profession. Here are the last lines of the Hippocratic Oath, to which physicians swear as the enter the profession. Highlighting added.
...Into whatsoever houses I enter, I will enter to help the sick, and I will abstain from all intentional wrong-doing and harm, especially from abusing the bodies of man or woman, bond or free. And whatsoever I shall see or hear in the course of my profession, as well as outside my profession in my intercourse with men, if it be what should not be published abroad, I will never divulge, holding such things to be holy secrets.
Now if I carry out this oath, and break it not, may I gain for ever reputation among all men for my life and for my art; but if I break it and forswear myself, may the opposite befall me.
The concerns about being "found out" often have less to do with the healthcare providers than of oneself. There is a pervasive human fear of being unworthy--and worse of being found out to be unworthy-- of being "not good enough". That experience is universal, and to some extent underpins why swinging is a somewhat secretive alternative lifestyle. Swinging is about consenting adults at play. Yet if our behaviors and out preferences were found out, we would not only be judged but shamed. This is the consequence of not conforming to social norms. The dependence on external validation in order (for example) to earn a living gets convolved with the covenantal relationships of the healing professions and creates its own tension: public lives and private lives are always complementary and essentially never congruent. Yet those in the healing professions have to understand both because so much of healing involves reaching some sort of personal reconciliation. That reconciliation requires embrace of something that makes most (all?) of us uncomfortable--it requires embrace of vulnerability.
The sociologist Brene' Brown is widely recognized for her research into vulnerability. As a start, it's a fun 20 minutes listening to her widely praised TED talk here:
The talk is a decade old, and still worth a re-listen.
Good luck.