They're your family after all and your family will care for you and support you more than anyone else because they're your family. As opposed to a counsellor who ultimately doesn't care about you, she cares about her salary.

It sounds like you're looking to blame anyone and everyone for your addiction and going to see a female counsellor to talk about sex is probably not helping. You might end up fantasising about having sex with her...

Your poor wife has to put up with you and your problems so you should probably give her more credit. Babysitting a fully grown man with mental health problems cannot be easy on her.

As for your daughter, she is 19. She can understand that people have issues and I'm sure she will take it just fine, as long as you don't break down in front of her or anything. Whether she chooses to tell her friends about you is her choice although I doubt she will, as you said mental illness does have a certain overtone.

I'd also suggest not telling her about the sex addiction, she doesn't need to know that. Tell her you're just going to counselling for anxiety. She won't know any better. Just remember when you feel miserable or upset or whatever, think about the people around you, imagine if the shoe was on the other foot, your patience would wear thin too wouldn't it?

Good luck