Dear Amulu,
Why can't you go for waxing? You can't find a beauty parlour nearby or they won't allow you to go to one?
You cannot remove that darkness with home remedies. It will not go dear. Only waxing can prevent as Neya said. Or go in for epilators which are available in the shops.
Do one thing. Get cold wax from the shop, warm it over hot water. Apply that to your underarms and then pull it off with a thick cloth. But you have to get someone to help you to do this. Since it is a delicate area it will be painful if you do it alone.
Just go to this site for more details
Dark Underarm
Love
Latha