How To Treat Black Nape?

i have black nape, and underarms. i can't ponytail my hair in school because im too shy when my classmates see my black nape. and i wanted to wear sleeveless ever since, but i have black armpit. and prom night is fast approaching. how can i get my pits and nape white for just a short period of time without using chemicals or something that will cost much money? I'm 14, 4"9, 56 kg