discolored flap of stretchy skin in my vagina?

It is your inner lips (labia minora). They come in all shapes, lengths, and colors. In short, they are as unique as any other body part on your body.

Normally they are also asymmetrical.

I had read somewhere that it could be my hymen. Besides, shouldn't the labia minora be two flaps of skin? Not one, like I have?

EDIT: I just washed my hands and checked. I'm pretty sure it's not the labia minora. For one thing, it is one large flap, not two. Secondly, it is located in the center (perhaps a little down) of my vagina. The labia minora are like doors, correct? They open into the vaginal orifice. This doesn't do this.

Hypothetically, if it was my hymen, what should/where should the hymen be located?

Your hymen covered your vaginal entrance while you grew in your mother's womb. What was inside the hymen was your insides, what was outside was your outsides. It is literally located where your insides and outsides came together.

As such it is around the outside edge of your vaginal entrance, not deep inside. It is certainly possible that it can tear lose on one side and hang down. It can also be a septate hymen, or a septate hymen where the fleshy bridge broke lose.