I can't imagine that professionals will encourage your dd to indulge in attention seeking or feel sorry for herself, or that they will rush to prescribe medication to an 11yo.
My dd has suffered from severe anxiety for many years. The CAHMS people did everything they could to avoid prescribing anything, and only agreed to do so once she got to 15. They explained exactly why they were cautious, what the dangers are and how limited the drugs are that you can prescribe for young people: if we hadn't been happy they wouldn't have done it. They worked with CBT for over 18 months first and if CBT alone could have done it then nobody would ever have thought of medication. It turned out dd needed a stronger approach and in the end it was we who asked for medication.
She is still having the CBT sessions and as far as I can see, they are very much about getting dd to take responsibility for her own issues rather than dumping on other people and showing her ways in which she can do that. About as far from encouraging attention seeking as you can imagine.
In a way, I can understand your frustration. Having mental health problems in the family is a massive drain on the whole family. I often feel like screaming and running. But years of struggle have taught me that no amount of denial will cure dd; the problem simply won't go away because I refuse to see it. In that respect it is no different from any other illness. SILs cancer is also a great inconvenience to her cancer. But she can't make the problem go away by refusing to see her doctor.
The good news is that we are seeing a slow improvement. Dd does seem a little more willing to believe that things can be worked out, she is less liable to freak out and easier to talk out of freak mode.
Like your dd she is intelligent, used to working hard, has had a (fairly) privileged upbringing, has been showered with love all her life. It hasn't made the difference between her developing an anxiety disorder and staying well. But it may just have made the difference between her still being alive and...not being alive. And that has to count for something. Whenever I feel like a failure because my daughter, my daughter! has a mental health problem, I remind myself that my daughter (the one I love and am proud of!) is still alive and fighting.