I agree with those above. If it ain't broke , don't fix it. I too have added a second therapist. I did it under my T recommendation because of my eating disorder. She, the 2nd t, is very helpful, and it really seems to be helping the ED, but I couldn't manage her, or my life, without my regular T. I don't think it will always be this way. It's just how I feel right now.
I've talked to my T about my feelings of dependency on both therapy and him. I don't like that needy feeling. As Evangelistie pointed out, however, it's a part of therapy to learn that you can trust and depend on other people. When we're ready, the next stage is learning to internalize those relationships, and feel we can hear those voices within us, and depend on a blend of those voices and ourselves.
Your discussion of your anger toward yourself, and the resulting self-injury, I identify with completely. I, too, have only recently learned to start directing the anger outward. It points to wonderful progress and growth on your part that you are working through this. I wouldn't want to do anything to undermine that progress. I think it's possible that your therapist would be much more in tune with your needs then your psychiatrist. The psychiatrist is a medical physician, with only a smattering of psychotherapeutic training. I think discussing it with your t and getting her input would be the most important factor. Find what it is you both agree would be in your best interest, with the psychiatrist as a distant 3rd in terms of importance.
Hope things continue to go well for you.
Take Care, Quay