When I first told a doctor about my SH I wrote it down and gave it to them because I couldn't say it out loud. With time it does get easier to talk about but I think it's a great idea to write it down and give it to the doctor if you don't think you can say it. Keep in mind that most doctors have had some experience with SH so most of them will act appropriately.
They should know so they can help you. I too once felt like it wasnt anyones business but I think that's because we are almost possessive of our SH because it's been our secret for so long that we find it unatural for anyone else to know.
Try not to be hard on yourself. These things are hard to talk about, especially at first. For the first few months of therapy I would come in with things I had written and let her read it but eventually I didn't need to do that anymore and was able to say what I needed to.