You should have skin around your vagina, and here's why. First, you'll notice that you've got two bigger lips on your vagina.
In addition to these, you should have a slightly smaller pair of inner lips - often described as 'extra skin' or 'wrinkles'. This is a normal shape for a vagina.
These lips may be slightly uneven, longer than the outer lips, or small and tucked away. Pretty much anything goes, though if you have concern a doctor would be able to offer medical advice.
This cannot and should not be removed unless it poses a medical problem, and it's unlikely that would be the situation.
Basically, just take some time to get familiar with your individual look - hand mirrors are great for this. Once you're more familiar with your vagina, you'll probably be more comfortable with it as well.
Best of luck.