I'm so confused.

It sounds like it's your ueturine wall. The reason you have a period is because your uterus gets thick to carry a baby. If you don't get pregnant is sloughs all of it off. They are usually called clots. Sometimes you will get larger ones like the size of a quarter, and other times they will be small enough that you won't see them. If you're worried about it or if it really doesn't look right then maybe go see a doctor. It sounds like a normal period to me though.

It might not even be your hymen. It could be your uterine wall which sheds when you have your period. Some months it's more visible than others. If it is your hymen, then I'm not sure why it would come out...I always thought it just tore, not fell off.

I'm not a doctor...but my guess would probably be that it had become stuck and couldn't release itself until your first menstrual cycle. OR...it was skin that had been chaffed away during sex that was loosened, but did not release itself until your period. Either way, you're not falling apart, and there is nothing wrong. However, if you bleed a lot after sex (by a lot, I mean often at times after having sex), then he is probably too big or you are extremely small there. If you're still scared, go to your gynecologist, but I'm sure she will tell you it's perfectly normal.