Sorry, but I have no clue about how birth control shows any hormone levels, I don't do any birth control myself.
What's that method called anyway? I don't know, if I can be of any help with photos either.
I don't think you need to worry about being intersex that much, if you have periods and normal hormone levels without taking hormone pills.
But there shouldn't be made any "diagnosis" via internet, so I'd highly recommend you to go seeing a doctor, if you want to be sure - all the more if your immune system is weak!
Your family doctor should be able to have a first look at you and may send you to an endocrinologist for further checks, if anything is fishy.
Well I'm German though, so I don't know much about American birth control methods and am used to health insurance covering checks.
I hope everything will work out for you.

Good Night,
Alex