That's because you're simply adorable, Dr. Wilson.
When I was a doctor and I had patients or patient's family members flirt I would mention that what they felt was not true attraction but emotional transference and that due to our code of ethics it absolutely could and would not happen.
That usually stopped the flirting, but when it didn't I would tell them directly I was in a committed relationship with my boyfriend, or girlfriend, or sometimes both to shake the story up, and I wasn't interested in adding a another party to that.