I talked to the girl very erotically during the doctor's appointment
Why would you do that in a setting like that?
She was asking me whether I liked her shirt, I had to tell her that she looked sexy in it
Those comments are inappropriate for that setting. That is harassment, you should not say that.
Do you think she was embarrassed?
She could have been. That is not something you want to hear from a patient. Next time, keep comments like that to yourself.