The Phoenix is a cool design I would not change her but the font for "Eastern Medicine Center" is a little block like. The Phoenix on top of it flows just possibly use a different font for the "Easter Medicine Center" part. Purple and Black are our colors so good job. I don't know if I like the color of the circle behind her I would try other colors to see if it works better it might just be that this is the best combo though, but lets see.
l like how the X looks like a tail but the phoenix font needs to be more asian or brush stroke like. The purple color is great but experiment with more color in the logo possibly one bleeding into the other. You don't need too many colors but maybe one more.