This is correct. This is a reflexive verb that you are doing to yourself. This translates to, "Normally I brush the hair". If it was something like "Normalmente me cepillo el pelo de Anna" it would be incorrect because you are doing it to Anna, not yourself.
el problema es que angela era alérgica a su medicamento, por lo que su médico le dio un nuevo medicamento que la mejoró porque no era alérgica a él
