In my job as a child care provider, I've noticed that it's very common for little girls discover themselves, sometimes even as early as two y.o. Perfectly natural, perfectly normal.
I think the previous posters have pointed out the most important piece of all: this is a great time to educate and teach your daughter about a little self-care. Handwashing/good hygiene is most important. You might also let her know that fingers are fine, but that she shouldn't use any toys or other items to touch her private parts with. I'm sure she's heard of germs/bacteria at this point, and can understand that they love to grow in nice dark warm areas of the body, including ears, bellybuttons, noses and also around her vagina and bottom. (or whatever terminology you use at home).
She may also be scratching herself because rashes itch and kids generally have very little self-control when it comes to not scratching. (I've seen this too! culprit=yeast.)
If it were me, I would take her in for a urine screen and to be checked for yeast. Some girls will develop a yeast infection without the symptoms we women typically associate with it. So please, get her checked out, or at least call your advice nurse.
In regard to the stinging during urination, I might suggest digging out your peri-bottle (from the hospital, given to mothers after a vaginal birth), if you received/have one,or some other clean squeeze bottle. Teach/help her to fill it with warm water before going to the bathroom. She can use it while she urinates to relieve the stinging and lower the acidity of the urine in contact with the skin. I know that it saved me time and time again after the birth of my son, or I would have dreaded using the bathroom even more!
I hope your issue resolves easily.