If your LCM had come to you and said, "I'd like you to go see my boyfriend, who is a psychiatrist, because he's starting up his own private practice and needs some clients to help out financially." then you'd have reason to be a bit miffed. But from what you've seemed to have indicated, she simply referred you to a psychiatrist, who she thinks would be a good fit for you and who she feels is a competent professional.

You don't mention that she told you this was her "boyfriend" that she was referring you to. I don't know about you, but if I'm going to a good doc or a good therapist, I want my friends and family to know how good that person is and I often refer them to the professional. I also refer them to solid, competent professionals that I know through my job or that I've met socially. I'm guessing, from how protective and nurturing your LCM has been with you, that she simply wanted you to have the benefit of seeing someone she respects and thinks is a good psychiatrist. She didn't mess up the referral by saying, "Hey, I'm dating this really awesome psychiatrist and I want you to go see him." Personally, her letting you know her personal relationship with the guy would have probably caused this exact messy situation or would have put undue pressure on you to comply.

As for her going to her daughter's concert, that's a given. Family always comes first, as painful as that might be to us clients! It would have been nice if she let you know that she was going to be there for a concert but I'm sorry, she doesn't owe you that. She has the right to have a life outside of her relationship with you. The best thing to do is talk about the pain with her and work through it.