I too think you should be fully evaluated before you invest a large sum in pilot training. It's possible you would qualify, and then at some future time fail, throwing all your plans into disarray. Best to work it through now.
Anemia to your degree, with Hgb below 9, virtually always has a reason, usually a simple one, occasionally complex. Once you know that reason, you and your AME's will be in a better position to make a decision about flight training.
Best of luck to you.
(still willing to comment on these things here!)