Minor cannot become intermedia, but from your description of the facial changes etc., I would say she was an obvious intermedia at a young age. There is a rare dominant beta gene which can cause a more serious transfusing requiring condition, but as I said, this is rare. The triplicated alpha globin gene combined with beta minor can also produce a more serious condition, and this diagnosis is becoming more commonly made in those with intermedia as mutations of the alpha genes are examined along with deletions. A DNA analysis would tell precisely which mutations or deletions are present. The DNA analysis should be of both chromosome 11 and 16, and the lab should be aware that they need to look for an alpha mutation, because often only deletions are noted.
Your previous doctors are typical in that they are not well informed about thalassemia. Many have never seen cases of transfusing thals, so it is understandable that they have not studied thalassemia. Even many hematologists are not well versed in the subject. A complete blood count and hemoglobin electrophoresis, and possibly a full iron panel, should be run. These results can show if a DNA analysis is needed. A hemoglobin level under 6 should set off alarms that every doctor should notice. Under 5 is getting into a dangerous zone where intervention with transfusion should already have taken place. Her care should have been much better all along. It is troubling that her doctors over the years have not done more to help her.