Amenorrhea -> FSH -> High -> Karyo
XY
If there is breast development, palpable inguinal mass (testes) = Androgen insensitivity. The excess testosterone is converted to estrogen so they get thelarche.
No breast development, sexual infantilism until puberty = 5-alpha reductase deficiency. At puberty they will virilize but will have female genitalia (which may virilize at that time). Will have normal internal male genitalia on US. (As an aside, I remember from college that there's some South American population where this is common, and they are called 'Machihembras.' That tidbit always helps me to remember it anyway..)
XX
Amenorrhea with secondary sexual development = Anatomic anomalies - Imperforate septum, transverse, Mullerian Agenesis (aka Muller-Rochitansky, whatever it's called syndrome)
Amenorrhea low test and estrogen = Savages syndrome - failure of ovaries to respond to LH/FSH
Amenorrhea high testosterone, almost 0 estrogen = Aromatase deficiency - normal internal genitalia, ambiguous external genitalia that may virilize. Of note, it can affect the mom in utero and virilize her.
Ultrasound is a good next test in general because it let's you check to see if there are mullerian structures (which will not be present in XY patients because the Y chromosome has the SRY gene which secretes Mullerian-Inhibitory Factor which destroys these) and because it let's you see if there are tested present.
Hope this helps.