I want to apply to a doctoral program in mathematics (I am currently a master's student) that is strong in algebra. The schools I found that have what I am interested in are "tier 1" schools with very competitive admissions and I am not sure what to do to improve my application. I had to withdraw a semester after my first year of graduate school because of several health problems, and when I went to the doctor I was told I had severe iron deficiency anemia as well as another medical issue I do not want to discuss here. I had it for almost ten years, but my previous doctor never diagnosed it. My GPA has suffered a lot from its side effects (it is 3.3) and also my subject GRE from undergrad is terrible (560). I was not able to retake the subject GRE because of a time conflict.
I want to apply for Fall 2016 because my health is a lot better now, but I am not sure what to do to make my application better. I feel like if I try to explain my health issue it will look like I am trying to make excuses. I have done seminar presentations, gone to an algebra conference, and done independent work without a faculty adviser (they always seem to tell me they are too busy or that I should stop studying material outside of classwork).
If someone can offer a suggestion on how I should approach explaining my situation or could suggest something for me to do to make myself more competitive, it would really help.
