I have something growing between my vagina and anus, its like a excess flesh.

It could be a skin tag if it's movable and not painful (otherwise some sort of cyst, ingrown hair, etc, if it did hurt). Very common. Usually not worth having removed. You can get skin tags anywhere on the body, but bumps and such occur a lot wherever there is constant moisture and closed in areas.

I am not diagnosing; this is just a guess. Have a doctor look at it now or when you next have a pap smear.

It does not hurt, but I'm scared that its like falling out of my skin.

Could it be coming out of your anus, a hemorrhoid? Those are common and mostly harmless too. You can apply PrepH or witch hazel, astringents.

Can you explain better what falling out of your skin looks like and whether it might really be at your rear rather than near your vagina?

Its like a horizontal wrinkle line in my perineum. I don't know how to explain better. But it really looks like a excess skin. Its so small but it flaps when I touch it. Its like its ready to get cut. Is this normal?

A guess - it is just plain old extra skin. Get on some dermatology sites and look at pictures starting with skin tags and papillomas. Some people get extra skin and bumps in the crotch, armpits, and under breasts.