Hi
Welcome to healthcareMagic.
You probably had a reaction to the dish soap you used.Dish soap has strong chemical when compared to body bathing soaps and so can cause irritation when come in contact with sensitive areas like eyes , lips , genitals.You could be having an infection on top of it which can be confirmed on examination.
i advise you to visit your Gynecologist and get treatment regimen.She may advise a
topical steroid cream using which symptoms come down.Meanwhile keep drinking plenty of fluids to reduce infection if any.
Take care.