Stinging period blood?

It could be that the blood sat around the vaginal opening too long - menstrual blood is no less hygienic than any other vaginal fluid, menstrual blood alone won't cause problems but ANY bodily fluid left sitting on the skin for too long can cause irritation (just like babies get diaper rash from urine sitting in contact with their skin too long).

It could also be if you've over-wiped or over-cleaned your vulva, lots of women do this because of paranoia over cleanliness during their periods, this can lead to irritation. If you use disposable pads like Always or Kotex these can cause moistness by preventing air-flow which can cause irritation like above mentioned diaper-rash like situation, also disposables are often chemically treated which can cause irritation or allergic reaction too.

The vaginal opening and the urethra are both in the vestibule of the vulva, so it may be that the urethra is stinging rather than the vaginal opening - watch for symptoms of a urinary tract infection like needing to pee more frequently even when little urine comes out, if this happens see your doctor. For now drink lots of water, change pads often, stay clean and dry (pat dry after you use the bathroom, avoid rubbing with toilet paper), and try over-the-counter vaginal irritation cream...even if no itching a vaginal cream may still help to ease soreness.